The Observable Signature of Black Hole Formation

Anthony L. Piro


Author: Anthony L. Piro

Affiliation: Theoretical Astrophysics Including Relativity (TAPIR), California Institute of Technology, Pasadena, USA

Black holes are among the most exciting objects in the Universe. They are regions of spacetime predicted by Einstein's theory of general relativity in which gravity is so strong that it prevents anything, even light, from escaping. Black holes are known to exist and roughly come in two varieties. There are massive black holes at the centers of galaxies, which can have masses anywhere from a million to many billion times the mass of our Sun. And there are also black holes of around ten solar masses in galaxies like our own that have been detected via X-ray emission from accretion [1]. Although this latter class of black holes is generally believed to be formed from the collapse of massive stars, there is a lot of uncertainty that is the focus of current ongoing research. It is unknown what fraction of massive stars produce black holes (rather than neutron stars), what the channels for black holes formation are, and what corresponding observational signatures are expected. Through a combination of theory, state-of-the-art simulations, and new observations, astrophysicists are trying to address these very fundamental questions.

A computer-generated image of the light distortions created by a black hole [Image credit: 
Alain Riazuelo, IAP/UPMC/CNRAS]

The one instance where astronomers are fairly certain they are seeing black hole formation is in the case of gamma-ray bursts (GRBs). A GRB is believed to be the collapse of a massive, quickly rotating star that produces a black hole and relativistic jet. The problem is that these are too rare and are too confined to special environments to explain the majority of black holes. Astronomers regularly see stars exploding as supernovae, but it is not clear what fraction of any of these produce black holes. There is evidence, and it is generally expected, that in most cases these explosions in fact lead to neutron stars instead. This has led to the hypothesis that the signature of black hole formation is in fact the disappearance of a massive star, or "unnova," rather than an actual supernova-like event [2].

My theoretical work [3] hypothesizes that there may be an observational signature of black hole formation, even in circumstances where one might normally expect an unnova. Therefore I titled my work "Taking the 'Un' out of 'Unnovae'." The main idea is based on a somewhat forgotten theoretical study by D. Z. Nadezhin [4]. Before a black hole is formed within a collapsing star, a neutron star is formed first. This neutron star emits neutrinos [5,6], which stream out of the star (because neutrinos are very weakly interacting) carrying energy (and thus mass via E=mc²). This can last for a few tenths of a second before enough material falls onto the neutron star to collapse it to a black hole, and carrying away a mass equivalent to a few tenths of the mass of our Sun. From the point of view of the star's envelope, it sees the mass (and therefore gravitational pull) of the core abruptly decrease and the envelope expands in response. This adjustment of the star's envelope grows into a shock wave that heats and ejects the outer envelope of the star.

This process was also looked at in detail by Elizabeth Lovegrove and Stan Woosley at UC Santa Cruz [7]. They were focused on the heating and subsequent cooling of the envelope from this shock. They found that it would lead to something that looked like a very dim supernova that would last for about a year. In my work, I focused on the observational signature when this shock first hits surface of the star. When this happens, the shock's energy is suddenly released in what is called a "shock breakout flash." Although this merely lasts for a few days, it is 10 to 100 times brighter than the subsequent dim supernova. Therefore, this is the best opportunity for astronomers to catch a black hole being created right in the act.

The most exciting part of this result is that now is the perfect time for astronomers to discover these events. Observational efforts such as the Palomar Transient Factory (also known as PTF) and the Panoramic Survey Telescope and Rapid Response System (also known as Pan-STARRS) are surveying the sky every night and sometimes finding rare and dim explosive, transient events. These surveys are well-suited to find exactly the kind of event I predict for the shock breakout from black hole formation. Given the rate we expect massive stars to be dying, it is not out of the question that one or more of these will be found in the next year or so, allowing us to actually witness the birth of a black hole.

References:
[1] Ronald A. Remillard and Jeffrey E. McClintock, "X-Ray Properties of Black-Hole Binaries". Annual Review of Astronomy & Astrophysics, 44, 49-92 (2006). Abstract.
[2] Christopher S. Kochanek,John F. Beacom, Matthew D. Kistler, José L. Prieto, Krzysztof Z. Stanek, Todd A. Thompson, Hasan Yüksel, "A Survey About Nothing: Monitoring a Million Supergiants for Failed Supernovae". Astrophysical Journal, 684, 1336-1342 (2008). Fulltext.
[3] Anthony L. Piro, "Taking the 'Un' out of 'Unnovae'". Astrophysical Journal Letters, 768, L14 (2013). Abstract.
[4] D. K. Nadyozhin, "Some secondary indications of gravitational collapse". Astrophysics and Space Science, 69, 115-125 (1980). Abstract.
[5] Adam Burrows, "Supernova neutrinos". Astrophysical Journal, 334, 891-908 (1988). Full Text.
[6] J. F. Beacom, R. N. Boyd, and A. Mezzacappa, "Black hole formation in core-collapse supernovae and time-of-flight measurements of the neutrino masses". Physical Review D, 63, 073011 (2001). Abstract.
[7] Elizabeth Lovegrove and Stan E. Woosley, "Very Low Energy Supernovae from Neutrino Mass Loss". Astrophysical Journal, 769, 109 (2013). Abstract.

New Mass Limit for White Dwarfs: Explains Super-Chandrasekhar Type Ia Supernovae

Upasana Das (left) and Banibrata Mukhopadhyay (right)







Authors: Upasana Das and Banibrata Mukhopadhyay

Affiliation: Dept of Physics, Indian Institute of Science, Bangalore, India

Background:

Extremely luminous explosions of white dwarfs, known as type Ia supernovae [1], have always been in the prime focus of natural science. Generally, they are believed to result from the violent thermonuclear explosion of a carbon-oxygen white dwarf, when its mass approaches the famous Chandrasekhar limit of 1.44M_⊙ [2], with M_⊙ being the mass of Sun. The observed luminosity is powered by the radioactive decay of nickel, produced in the thermonuclear explosion, to cobalt and then to iron. The characteristic nature of the variation of luminosity with time of these supernovae (see Figure 1) -- along with the consistent mass of the exploding white dwarf -- allows these supernovae to be used as a ‘standard’ for measuring far away distances (standard candle) and hence in understanding the expansion history of the universe.

Figure 1: Variation of luminosity as a function of time of a type Ia supernova [image courtesy: Wikipedia]

Observation and study of this very feature of distant supernovae led to the Nobel Prize in Physics in 2011 for the discovery of the accelerated expansion of the universe [3, 2Physics report]. Also, mainly because of the discovery of the limiting mass of white dwarfs, S. Chandrasekhar was awarded the Nobel Prize in Physics in 1983.

Chandrasekhar, by means of a remarkably simple calculation, was the first to obtain the maximum mass for a (non-magnetized, non-rotating) white dwarf [2]. So far, observations seemed to abide by this limit. However, the recent discovery of several peculiar type Ia supernovae -- namely, SN 2006gz, SN 2007if, SN 2009dc, SN 2003fg [4,5] -- provokes us to rethink the commonly accepted scenario. These supernovae are distinctly over-luminous compared to their standard counterparts, because of their higher than usual nickel mass. They also violate the ‘luminosity-stretch relation’ and exhibit a much lower velocity of the matter ejected during the explosion. However, these anomalies can be resolved, if super-Chandrasekhar white dwarfs, with masses in the range 2.1-2.8M_⊙, are assumed to be the mass of the exploding white dwarfs (progenitors of these peculiar supernovae). Nevertheless, these non-standard ‘super-Chandrasekhar supernovae’ can no longer be used as cosmic distance indicators. However, there is no estimate of an upper limit to the mass of these super-Chandrasekhar white dwarf candidates yet. Can they be arbitrarily large? Moreover, there has been no foundational level analysis performed so far, akin to that carried out by Chandrasekhar, in order to establish a super-Chandrasekhar mass white dwarf.

Our result at a glance:

We establish a new and generic mass limit for white dwarfs which is 2.58M_⊙ [6]. This is significantly different from that proposed by Chandrasekhar. Our discovery naturally explains the over-luminous, peculiar type Ia supernovae mentioned above. We arrive at this new mass limit by exploiting the effects of the magnetic field in compact objects. The motivation behind our approach lies in the discovery of several isolated magnetized white dwarfs through the Sloan Digital Sky Survey (SDSS) with surface fields 10⁵-10⁹ gauss [7,8]. Hence their expected central fields could be 2-3 orders of magnitude higher. Moreover, about 25% of accreting white dwarfs, namely cataclysmic variables (CVs), are found to have magnetic fields as high as 10⁷-10⁸ gauss [9].

Underlying theory:

We first recall the basic formation scenario of white dwarfs. In order to do so, we have to understand the properties of degenerate electrons. When different states of a particle correspond to the same energy in quantum mechanics, they are called degenerate states. Moreover, Pauli’s exclusion principle prohibits any two identical fermions (in the present context: electrons) to occupy the same quantum state. Now, when a normal star of mass less than or of the order of 5M_ʘ exhausts its nuclear fuel [10], it undergoes a collapse leading to a small volume consisting of a lot of electrons. Being in a small volume, many such electrons tend to occupy the same energy states, and hence they become degenerate, since the energy of a particle depends on its momentum which is determined by the total volume of the system. Hence, once all the energy levels up to the Fermi level, which is the maximum allowed energy of a fermion, are filled by the electrons, there is no available space for the remaining electrons in a small volume of the collapsing star. This expels the electrons to move out leading to an outward pressure. If the force due to the outward pressure is able to balance the inward gravitational force, then the collapse halts, forming the compact star white dwarf.

Figure 2: Landau quantization in presence of magnetic field B. [image courtesy: Warwick University, UK ]

For the current purpose, we have to also recall the properties of degenerate, relativistic electrons under the influence of a strong magnetic field, neglecting any form of interactions. The energy states of a free electron in a magnetic field are quantized into what is known as Landau orbitals [11]. Figure 2 shows that how the continuous energy levels split into discrete Landau levels with the increase of magnetic field in the direction perpendicular to the motion of the electron. Larger the magnetic field, smaller is the number of Landau levels occupied. Recent works [12-14] establish that Landau quantization due to a strong magnetic field modifies the equation of state (EoS), which relates the pressure (P) with density (ρ), of the electron degenerate gas. This should influence significantly the mass and radius of the underlying white dwarf (and hence the mass-radius relation). The main aim here is to obtain the maximum possible mass of such a white dwarf (which is magnetized), and therefore a (new) mass limit. Hence we look for the regime of high density of electron degenerate gas and the corresponding EoS, which further corresponds to the high Fermi energy (E_F) of the system. This is because the highest density corresponds to the lowest volume and hence, lowest radius, which further corresponds to the limiting mass [2]. Note that the maximum Fermi energy (E_Fmax) corresponds to the maximum central density of the star. Consequently, conservation of magnetic flux (technically speaking flux freezing theorem, which is generally applicable for a compact star) argues for the maximum possible field of the system, which implies that only the ground Landau level will be occupied by the electrons.

Generally the EoS can be recast in the polytropic form of P=Kρ^Γ, when K is a constant and Γ (=1+1/n) is the polytropic index. At the highest density regime (which also corresponds to the highest magnetic field regime), Γ=2. Now combining the above EoS with the condition of magnetostatic equilibrium (when net outward force is balanced by the inward force), we obtain the mass and radius of the white dwarf to scale with its central density (ρ_c) as M ∝ K^(3/2) ρ_c^(3-n)/2n and R ∝ K^(1/2) ρ_c^(1-n)/2n respectively [6]. For Γ = 2, which corresponds to the case of limiting mass, K ∝ ρ_c^(-2/3) and hence M becomes independent of ρ_c and R becomes zero. Substituting the proportionality constants, for Γ = 2 we obtain exactly [6]:

where h is the Planck’s constant, c the speed of light, G Newton’s gravitation constant, μ_e the mean molecular weight per electron and m_H the mass of hydrogen atom. For μ_e=2, which is the case for a carbon-oxygen white dwarf, M≈2.58M_⊙. To compare with Chandrasekhar’s result [2], we recall the limiting mass obtained by him as

which for μ_e =2 is 1.44M_⊙.

Figure 3: Mass-radius relation of a white dwarf. Solid line – Chandrasekhar’s relation; dashed line – our relation.

For a better reference, we include a comparison between the mass-radius relation of the white dwarf obtained by Chandrasekhar and that obtained by us in Figure 3.

Justification of high magnetic field and its effect to hold more mass:

The presence of magnetic field in a white dwarf creates an additional outward pressure apart from that due to degenerate electrons, which is however modified in presence of a strong field in it. On the other hand, the inward (gravitational) force is proportional to the mass of the white dwarf. Hence, when the star is magnetized, a larger outward force can balance a larger inward force, allowing it to have more mass.

However, the effect of Landau quantization becomes significant only at a high field B ≥ B_c = 4.414×10¹³ gauss. How can we justify such a high field in a white dwarf? Let us consider the commonly observed phenomenon of a magnetized white dwarf attracting mass from its companion star (called accretion). Now the surface field of an accreting white dwarf, as observed, could be 10⁹ gauss (≪ B_c) [7]. Its central field, however, can be several orders of magnitude higher ∼ 10¹² gauss, which is also less than B_c. Naturally, such a magnetized CV, still follows the mass-radius relation obtained by Chandrasekhar. However, in contrast with Chandrasekhar’s work (which did not include a magnetic field in the calculations), we obtain that, a nonzero initial field in the white dwarf, however ineffective for rendering Landau quantization effects, proves to be crucial in supporting the additional mass accumulated due to accretion.

As an above-mentioned magnetized white dwarf first gains mass due to accretion, its total mass increases which in turn increases the gravitational power and hence the white dwarf contracts in size due to the increased gravitational pull. However, the total magnetic flux in a white dwarf is understood to be conserved, which is magnetic field times the square of its radius. Therefore, if the white dwarf shrinks, its radius decreases and hence magnetic field increases. This in turn increases the outward force balancing the increased inward gravitational force (due to increase of its mass), which leads to a quasi-equilibrium situation. As the accretion is a continuous process, above process of shrinking the white dwarf, increasing the magnetic field and holding more mass, goes in a cycle. This continues until the gain of mass becomes so great that total outward pressure is unable to support the gravitational attraction. This finally leads to a supernova explosion, which we observe as a peculiar, over-luminous type Ia supernova, in contrast to their normal counter parts.

Punch lines:

More than 80 years after the proposal of Chandrasekhar mass limit, this new limit perhaps heralds the onset of a paradigm shift. This discovery has several consequences as briefly described below.

The masses of white dwarfs are measured from their luminosities assuming Chandrasekhar's mass-radius relation, as of now. These results may have to be re-examined based on the new mass-radius relation, at least for some peculiar objects (e.g. over-luminous type Ia supernovae). Further, some peculiar known objects, like magnetars (highly magnetized compact objects, supposedly neutron stars, as of now) should be examined based on the above considerations, which could actually be super-Chandrasekhar white dwarfs.

This new mass limit may also lead to establishing the underlying peculiar supernovae as a new standard candle for cosmic distance measurement. Hence, in order to correctly interpret the expansion history of the universe (and then dark energy), one might need to carefully sample the observed data from the supernovae explosions, especially if the peculiar type Ia supernovae are eventually found to be enormous in number. However, it is probably too early to comment whether our discovery has any direct implication on the current dark energy scenario, which is based on the observation of ordinary type Ia supernovae.

References:
[1] D. Andrew Howell, “Type Ia supernovae as stellar endpoints and cosmological tools”, Nature Communications, 2, 350 (2011). Abstract.
[2] S. Chandrasekhar, “The highly collapsed configurations of a stellar mass (Second Paper)”, Monthly Notices of the Royal Astronomical Society, 95, 207 (1935). Article.
[3] S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro, S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman, R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz-Lapuente, N. Walton, B. Schaefer, B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M. Newberg, W. J. Couch, and The Supernova Cosmology Project, “Measurements of Omega and Lambda from 42 high-redshift supernovae”, The Astrophysical Journal, 517, 565 (1999). Article.
[4] D. Andrew Howell, Mark Sullivan, Peter E. Nugent, Richard S. Ellis, Alexander J. Conley, Damien Le Borgne, Raymond G. Carlberg, Julien Guy, David Balam, Stephane Basa, Dominique Fouchez, Isobel M. Hook, Eric Y. Hsiao, James D. Neill, Reynald Pain, Kathryn M. Perrett and Christopher J. Pritchet, “The type Ia supernova SNLS-03D3bb from a super-Chandrasekhar-mass white dwarf star”, Nature, 443, 308 (2006). Abstract.
[5] R. A. Scalzo, G. Aldering, P. Antilogus, C. Aragon, S. Bailey, C. Baltay, S. Bongard, C. Buton, M. Childress, N. Chotard, Y. Copin, H. K. Fakhouri, A. Gal-Yam, E. Gangler, S. Hoyer, M. Kasliwal, S. Loken, P. Nugent, R. Pain, E. Pécontal, R. Pereira, S. Perlmutter, D. Rabinowitz, A. Rau, G. Rigaudier, K. Runge, G. Smadja, C. Tao, R. C. Thomas, B. Weaver, and C. Wu, “Nearby supernova factory observations of SN2007if: First total mass measurement of a super-Chandrasekhar-mass progenitor”, The Astrophysical Journal, 713, 1073 (2010). Article.
[6] Upasana Das & Banibrata Mukhopadhyay, “New mass limit for white dwarfs: Super-Chandrasekhar type Ia supernova as a new standard candle”, Physical Review Letters, 110, 071102 (2013). Abstract.
[7] Gary D. Schmidt, Hugh C. Harris, James Liebert, Daniel J. Eisenstein, Scott F. Anderson, J. Brinkmann, Patrick B. Hall, Michael Harvanek, Suzanne Hawley, S. J. Kleinman, Gillian R. Knapp, Jurek Krzesinski, Don Q. Lamb, Dan Long, Jeffrey A. Munn, Eric H. Neilsen, Peter R. Newman, Atsuko Nitta, David J. Schlegel, Donald P. Schneider, Nicole M. Silvestri, J. Allyn Smith, Stephanie A. Snedden, Paula Szkody, and Dan Vanden Berk, “Magnetic white dwarfs from the Sloan Digital Sky Survey: The first data release”, The Astrophysical Journal, 595, 1101 (2003). Article.
[8] Karen M. Vanlandingham, Gary D. Schmidt, Daniel J. Eisenstein, Hugh C. Harris, Scott F. Anderson, Patrick B. Hall, James Liebert, Donald P. Schneider, Nicole M. Silvestri, Gregory S. Stinson, and Michael A. Wolfe, “Magnetic white dwarfs from the SDSS. II. The second and third data releases”, The Astronomical Journal, 130, 734 (2005). Article.
[9] D. T. Wickramasinghe and Lilia Ferrario, “Magnetism in isolated and binary white dwarfs”, Publications of the Astronomical Society of the Pacific, 112, 873 (2000). Article.
[10] S.L. Shapiro and S.A. Teukolsky, “Black holes, White dwarfs and Neutron stars: The physics of compact objects” (John Wiley & Sons Inc, 1983).
[11] Dong Lai and Stuart L. Shapiro, “Cold equation of state in a strong magnetic field – Effect of inverse beta-decay”, The Astrophysical Journal, 383, 745 (1991). Abstract.
[12] Upasana Das and Banibrata Mukhopadhyay, “Strongly magnetized cold degenerate electron gas: Mass-radius relation of the magnetized white dwarf”, Physical Review D, 86, 042001 (2012). Abstract.
[13] Upasana Das and Banibrata Mukhopadhyay, “Violation of Chandrasekhar mass limit: The exciting potential of strongly magnetized white dwarfs”, Int. J. Mod. Phys. D, 21, 1242001 (2012). Abstract.
[14] Aritra Kundu and Banibrata Mukhopadhyay, “Mass of highly magnetized white dwarfs exceeding the Chandrasekhar limit: An analytical view”, Modern Physics Letters A, 27, 1250084 (2012). Abstract.

Black Hole Evaporation Rates without Spacetime

Samuel L. Braunstein

Author: Samuel L. Braunstein

Affiliation: Professor of Quantum Computation, University of York, UK


Why black holes are so important to physics

In the black hole information paradox, Hawking pointed out an apparent contradiction between quantum mechanics and general relativity so fundamental that some thought any resolution may lead to new physics. For example, it has been recently suggested that gravity, inertia and even spacetime itself may be emergent properties of a theory relying on the thermodynamic properties across black hole event horizons [1]. All these paradoxes and prospects for new physics ultimately rely on thought experiments to piece together more detailed calculations, each of which themselves only give a part of the full picture. Our work "Black hole evaporation rates without spacetime" adds another calculation [2] which may help focus future work.

The paradox, a simple view

In its simplest form, we may state the paradox as follows: In classical general relativity, the event horizon of a black hole represents a point of no return - as a perfect semi-permeable membrane. Anything can pass the event horizon without even noticing it, yet nothing can escape, even light. Hawking partly changed this view by using quantum theory to prove that black holes radiate their mass as ideal thermal radiation. Therefore, if matter collapsed to form a black hole which itself then radiated away entirely as formless radiation then the original information content of the collapsing matter would have vanished. Now, information preservation is fundamental to unitary evolution, so its failure in black hole evaporation would signal a manifest failure of quantum theory itself. This "paradox" encapsulates a profound clash between quantum mechanics and general relativity.

To help provide intuition about his result Hawking presented a heuristic picture of black hole evaporation in terms of pair creation outside a black hole's event horizon. The usual description of this process involves one of the pair carrying negative energy as it falls into the black hole past its event horizon. The second of the pair carries sufficient energy to allow it to escape to infinity appearing as Hawking radiation. Overall there is energy conservation and the black hole losses mass by absorbing negative energy. This heuristic mechanism actually strengthens the "classical causal" structure of the black hole's event horizon as being a perfect semi-permeable (one-way) membrane. The paradox seems unassailable.

Scratching the surface of the paradox

This description of Hawking radiation as pair creation is seemingly ubiquitous (virtually any web page providing an explanation of Hawking radiation will invoke pair creation).

Nonetheless, there are good reasons to believe this heuristic description may be wrong [3]. Put simply, every created pair will be quantum mechanically entangled. If the members of each pair are then distributed to either side of the event horizon the so-called rank of entanglement across the horizon will increase for each and every quanta of Hawking radiation produced. Thus, one would conclude that just as the black hole mass were decreasing by Hawking radiation, its internal (Hilbert space) dimensionality would actually be increasing.

For black holes to be able to eventually vanish, the original Hawking picture of a perfectly semi-permeable membrane must fail at the quantum level. In other words, this "entanglement overload" implies a breakdown of the classical causal structure of a black hole. Whereas previously entanglement overload had been viewed as an absolute barrier to resolving the paradox [3], we argue [2,4] that the above statements already point to the likely solution.

Evaporation as tunneling

The most straightforward way to evade entanglement overload is for the Hilbert space within the black hole to "leak away". Quantum mechanically we would call such a mechanism tunneling. Indeed, for over a decade now, such tunneling, out and across the event horizon, has proved a useful way of computing black hole evaporation rates [5].

Spacetime free conjecture

In our paper [2] we suggest that the evaporation across event horizons operates by Hilbert space subsystems from the black hole interior moving to the exterior. This may be thought of as some unitary process which samples the interior Hilbert space; picks out some subsystem and ejects it as Hawking radiation. Our manuscript primarily investigates the consequences of this conjecture applied specifically to event horizons of black holes.

At this point a perceptive reader might ask how and to what extent our paper sheds light on the physics of black hole evaporation. First, the consensus appears to be that the physics of event horizons (cosmological, black hole, or those due to acceleration) is universal. In fact, it is precisely because of this generality that one should not expect this Hilbert space description of evaporation at event horizons to bear the signatures of the detailed physics of black holes. In fact, as explained in the next section we go on to impose the details of that physics onto this evaporative process. Second, sampling the Hilbert space at or near the event horizon may or may not represent fair sampling from the entire black hole interior. This issue is also discussed below (and in more detail in the paper [2]).

Imposing black hole physics

We rely on a few key pieces of physics about black holes: the no-hair theorem and the existence of Penrose processes. We are interested in a quantum mechanical representation of a black hole. At first sight this may seem preposterous in the absence of a theory of quantum gravity. Here, we propose a new approach that steers clear of gravitational considerations. In particular, we derive a quantum mechanical description of a black hole by ascribing various properties to it based on the properties of classical black holes. (This presumes that any quantum mechanical representation of a black hole has a direct correspondence to its classical counterpart.) In particular, like classical black holes our quantum black hole should be described by the classical no-hair properties of mass, charge and angular momentum. Furthermore, these quantum mechanical black holes should transform amongst each other just as their classical counterparts do when absorbing or scattering particles, i.e., when they undergo so-called Penrose processes. By imposing conditions consistent with these classical properties of a black hole we obtain a Hilbert space description of quantum tunneling across the event horizons of completely generic black holes. Crucially, this description of black hole evaporation does not involve the detailed curved spacetime geometry of a black hole. In fact, it does not require spacetime at all. Finally, in order to proceed to the next step of computing the actual dynamics of evaporation, we need to invoke one more property of a black hole: that of its enormous dimensionality.

Tunneling probabilities

The Hilbert space dimensionalities needed to describe a black hole are vast (at least 10¹⁰⁷⁷ for a stellar-mass black hole). For such dimensionalities, random matrix theory tells us that the statistical behavior of tunneling (as a sampling of Hilbert space subsystems) is excellently approximated by treating tunneling as a completely random process. This immediately imposes a number of symmetries onto our description of black hole evaporation. We can now completely determine the tunneling probabilities as a function of the classical no-hair quantities [2]. These tunneling probabilities are nothing but the black hole evaporation rates. In fact, these are precisely the quantities that are computed using standard field theoretic methods (that all rely on the curved black hole geometry). Thus, the calculation of tunneling probabilities provides a way of validating our approach and making our results predictive.

The proof of the pudding: validation and predictions

Our results reproduce Hawking's thermal spectrum (in the appropriate limit), and reproduce his relation between the temperature of black hole radiation and the black hole's thermodynamic entropy.

When Hawking's semi-classical analysis was extended by field theorists to include backreaction from the outgoing radiation on the geometry of the black hole a modified non-thermal spectrum was found [5]. The incorporation of backreaction comes naturally in our quantum description of black hole evaporation (in the form of conservation laws). Indeed, our results show that black holes that satisfy these conservation laws are not ideal but "real black bodies" that exhibit a non-thermal spectrum and preserve thermodynamic entropy.

These results support our conjecture for a spacetime free description of evaporation across black hole horizons.

Our analysis not only reproduces these famous results [5] but extends them to all possible black hole and evaporated particle types in any (even extended) gravity theories. Unlike field theoretic approaches we do not need to rely on one-dimensional WKB methods which are limited to the analysis of evaporation along radial trajectories and produce results only to lowest orders in ℏ.

Finally, our work quite generally predicts a direct functional relation exists between the irreducible mass associated with a Penrose process and a black hole's thermodynamic entropy. This in turn implies a breakdown in Hawking's area theorem in extended gravity theories.


And the paradox itself

The ability to focus on events horizons is key to the progress we have made in deriving a quantum mechanical description of evaporation. By contrast, the physics deep inside the black hole is more elusive. If unitarity holds globally then our spacetime free conjecture can be used to describe the entire time-course of evaporation of a black hole and to learn how the information is retrieved (see e.g., [6]). Specifically, in a unitarily evaporating black hole, there should exist some thermalization process, such that after what has been dubbed the black hole's global thermalization (or scrambling) time, information that was encoded deep within the black hole can reach or approach its surface where it may be selected for evaporation as radiation. Alternatively, if the interior of the black hole is not unitary, some or all of this deeply encoded information may never reappear within the Hawking radiation. Unfortunately, any analysis relying primarily on physics at or across the horizon cannot shed any light on the question of unitarity (which lies at the heart of the black hole information paradox).

The bigger picture

At this stage we might take a step back and ask the obvious question: Does quantum information theory really bear any connection with the subtle physics associated with black holes and their spacetime geometry? After all we do not yet have a proper theory of quantum gravity. However, whatever form such a theory may take, it should still be possible to argue, either due to the Hamiltonian constraint of describing an initially compact object with finite mass, or by appealing to holographic bounds, that the dynamics of a black hole must be effectively limited to a finite-dimensional Hilbert space. Moreover, one can identify the most likely microscopic mechanism of black hole evaporation as tunneling. Formally, these imply that evaporation should look very much like our sampling of Hilbert space subsystems from the black hole interior for ejection as radiation [2,4,6]. Although finite, the dimensionalities of the Hilbert space are immense and from standard results in random unitary matrix theory and global conservation laws we obtain a number of invariances. These invariances completely determine the tunneling probabilities without needing to know the detailed dynamics (i.e., the underlying Hamiltonian). This result puts forth the Hilbert space description of black hole evaporation as a powerful tool. Put even more strongly, one might interpret the analysis presented as a quantum gravity calculation without any detailed knowledge of a theory of quantum gravity except the presumption of unitarity [2].

Hints of an emergent gravity

Verlinde recently suggested that gravity, inertia, and even spacetime itself may be emergent properties of an underlying thermodynamic theory [1]. This vision was motivated in part by Jacobson's 1995 surprise result that the Einstein equations of gravity follow from the thermodynamic properties of event horizons [7]. For Verlinde's suggestion not to collapse into some kind of circular reasoning we would expect the physics across event horizons upon which his work relies to be derivable in a spacetime free manner. It is exactly this that we have demonstrated is possible in our manuscript [2]. Our work, however, provides a subtle twist: Rather than emergence from a purely thermodynamic source, we should instead seek that source in quantum information.

In summary, this work [2,4]:

• shows that the classical picture of black hole event horizons as perfectly semi-permeable almost certainly fails quantum mechanically
• provides a microscopic spacetime-free mechanism for Hawking radiation
• reproduces known results about black hole evaporation rates
• authenticates random matrix theory for the study of black hole evaporation
• predicts the detailed black hole spectrum beyond WKB
• predicts that black hole area must be replaced by some other property in any generalized area theorem for extended gravities
• provides a quantum gravity calculation based on the presumption of unitarity, and
• provides support for suggestions that gravity, inertia and even spacetime itself could come from spacetime-free physics across event horizons

References
[1] E. Verlinde, "On the origin of gravity and the laws of Newton", JHEP 04 (2011) 029. Abstract.
[2] S.L. Braunstein and M.K. Patra, "Black Hole Evaporation Rates without Spacetime", Phys. Rev. Lett. 107, 071302 (2011). Abstract. Article (pdf).
[3] H. Nikolic, "Black holes radiate but do not evaporate", Int. J. Mod. Phys. D 14, 2257 (2005). Abstract; S.D. Mathur, "The information paradox: a pedagogical introduction", Class. Quantum Grav. 26, 224001 (2009). Abstract.
[4] Supplementary Material to [2] at http://link.aps.org/supplemental/10.1103/PhysRevLett.107.071302.
[5] M.K. Parikh and F. Wilczek, "Hawking Radiation As Tunneling", Phys. Rev. Lett. 85, 5042 (2000). Abstract.
[6] S.L. Braunstein, S. Pirandola and K. Życzkowski, "Entangled black holes as ciphers of hidden information", arXiv:0907.1190.
[7] T. Jacobson, "Thermodynamics of Spacetime: The Einstein Equation of State", Phys. Rev. Lett. 75, 1260 (1995). Abstract.

Beam Pulses Perforate Black Hole Horizon

Alexander Burinskii


[Every year (since 1949) the Gravity Research Foundation honors best submitted essays in the field of Gravity. This year's prize goes to Alexander Burinskii for his essay "Instability of Black Hole Horizons with respect to Electromagnetic Excitations". The five award-winning essays will be published in the Journal of General Relativity and Gravitation (GRG) and subsequently, in a special issue of the International Journal of Modern Physics D (IJMPD). Today we present here an invited article from Prof. Burinskii on his current work.
-- 2Physics.com ]



Author: Alexander Burinskii
Nuclear Safety Institute, Russian Academy of Sciences, Moscow, Russia

The variety of models of the black-hole (BH) evaporation process -- that appeared in recent years -- differ essentially from each other, as well as from Hawking’s original idea. However, they contain a common main point that the mechanism of evaporation is connected with a complex analyticity and conformal structure [1], which unifies the BH physics with (super)string theory and physics of elementary particles [2, 3].

It has been observed long ago that many exact solutions in gravity contain singular wires and beams. Looking for exact wave solutions for electromagnetic (EM) field on the Kerr-Schild background, we obtained results [4] which show that they do not contain the usual smooth harmonic functions, but acquire commonly singular beam pulses which have very strong back reaction to metric. Analysis showed [5] that the EM beams break the BH horizon, forming the holes connecting the internal and external regions. As a result, the horizon of a BH interacting with the nearby EM fields turns out to be covered by a set of holes [6, 7] and will be transparent for outgoing radiation. Therefore, the problem of BH evaporation acquires explanation at the classical level.

2Physics articles by past winners of the Gravity Research Foundation award:
T. Padmanabhan (2008): "Gravity : An Emergent Perspective"
Steve Carlip (2007): "Symmetries, Horizons, and Black Hole Entropy"

We consider BH metric in the Kerr-Schild (KS) form [8]: g_μν = η_μν + 2H k_μ k_ν, which has many advantages. In particular, the KS coordinate system and solutions do not have singularities at the horizon, being disconnected from the positions of the horizons and rigidly related with auxiliary Minkowski space-time with metric η_μν. The Kerr-Schild form is extremely simple and all the intricate details are encoded in the vortex vector field k_μ(x) which is tangent to the light-like rays of the Kerr Congruence (in fact, these rays are twistors of the Penrose twistor theory).

The vector field k_ν determines symmetry of space, its polarization, and in particular, direction of gravitational ‘dragging‘. The structure of Kerr congruence is shown in Fig.1.

FIG. 1: The Kerr singular ring and Kerr congruence formed by the light-like twistor-beams.

Horizons are determined by function:
H =(mr − ψ²)/(r² + a² cos²θ) , where the function ψ ≡ ψ(Y) is related with electromagnetic field, and can be any analytic function of the complex angular coordinate
Y= exp{iφ} tan(θ/2) which parametrizes celestial sphere. The Reference [8] showed that the Kerr-Newman solution is the simplest solution of the Kerr-Schild class having ψ = q =constant, the value of charge. However, any holomorphic function ψ(Y ) also leads to an exact solution of this class, and such a non-constant function on sphere has to acquire at least one pole which creates the beam. So, the electromagnetic field corresponding to ψ(Y ) = q / Y forms a singular beam along z-axis which pierces the horizons, producing a hole allowing matter to escape the interior of black hole. The initially separated external and internal surfaces of the event horizons, r₊ and r_-, turn out to be joined by a tube, conforming a single connected surface.

This solution may be easily extended to the case of arbitrary numbers of beams propagating in different angular directions Y_i = exp{i φ_i} tan(θ_i/2) , which corresponds to a set of the light-like beams destroying the horizon in different angular directions, via action of the function ψ(Y) in H. The solutions for wave beams have to depend on a retarded-time τ. Their back reaction to the metric is especially interesting. Some long-term efforts [4, 6, 7] led us to obtain such solutions of the Debney-Kerr-Schild equations [8] in the low-frequency limit, and finally, obtain the exact solutions consistent with a time-averaged stress-energy tensor [9]. These time-dependent solutions revealed a remarkable structure which sheds light on the possible classical explanation of the BH evaporation, namely, a classical analog of quantum tunneling. In the exact time-dependent solutions, a new field of radiation was obtained which is determined by regular function γ_(reg)(Y,τ). This radiation is akin to the well known radiation of the Vaidya `shining star' and may be responsible for the loss of mass by evaporation. At the same time, the necessary conditions for evaporation -- the transparence of the horizon -- are provided by the singular field ψ(Y,τ) forming the fluctuating beam-pulses. As a result, the roles of ψ(Y,τ) and γ_(reg)(Y,τ) are separated! The horizon turns out to be fluctuating and pierced by a multitude of migrating holes, see Fig. 2.

The obtained solutions showed that the horizon is not irresistible obstacle, and there should not be any information loss inside the black hole. Due to topological instability of the horizon, the black-holes lose their demonic image, and hardly they can be created in a collider. However, the usual scenarios of the collapse have to be apparently valid, since the macroscopic processes should not be destroyed by the fine-grained fluctuations of the horizon. The known twosheetedness of the Kerr metric, which was considered as a long time mystery of the Kerr solution, turns out to be matched perfectly with the holographic structure of space-time [9,10]. The resulting classical geometry produced by fluctuating twistor-beams may be considered as a fine-grained structure which takes an intermediate position between the classical and quantum gravity [9].

References:
[1] S. Carlip, "Black Hole Entropy and the Problem of Universality",
J. Phys. Conf. Ser.67: 012022, (2007), gr-qc/0702094.
[2] G. `t Hooft, "The black hole interpretation of string theory",
Nucl Phys. B 335, 138 (1990). Abstract.
[3] A. Burinskii, "Complex Kerr geometry, twistors and the Dirac electron",
J. Phys A: Math. Theor, 41, 164069 (2008). Abstract. arXiv: 0710.4249[hep-th].
[4] A. Burinskii, "Axial Stringy System of the Kerr Spinning Particle",
Grav. Cosmol. 10, (2004) 50, hep-th/0403212.
[5] A. Burinskii, E. Elizalde, S.R. Hildebrandt and G. Magli, "Rotating 'black holes' with holes in the horizon", Phys. Rev. D 74, 021502(R) (2006) Abstract; A. Burinskii, "The Kerr theorem, Kerr-Schild formalizm and multiparticle Kerr-Schild solutions", Grav. Cosmol. 12, 119 (2006), gr-qc/0610007.
[6] A. Burinskii, "Aligned electromagnetic excitation of the Kerr-Schild Solutions",
Proc. of MG12 (2007), arXiv: gr-qc/0612186.
[7] A. Burinskii, E. Elizalde, S.R. Hildebrandt and G. Magli,"Aligned electromagnetic excitations of a black hole and their impact on its quantum horizon", Phys.Lett. B 671 486 (2009). Abstract.
[8] G.C. Debney, R.P. Kerr and A.Schild, "Solutions of the Einstein and Einstein-Maxwell Equations",
J. Math. Phys. 10, 1842 (1969). Abstract.
[9] A. Burinskii, "Beam Pulse Excitations of Kerr-Schild Geometry and Semiclassical Mechanism
of Black-Hole Evaporation", arXiv:0903.2365 [hep-th] .
[10] C.R. Stephens, G. t' Hooft and B.F. Whiting, "Black hole evaporation without information loss", Class. Quant. Grav. 11, 621 (1994). Abstract.

Gravity : An Emergent Perspective

Author:
T. Padmanabhan

Affiliation: Inter University Centre for Astronomy and Astrophysics (IUCAA), Pune, India

Historically, we thought of electrons as particles and photons as waves, time as absolute and gravity as a force. Padmanabhan, in his recent work "Gravity-the Inside Story" which won the First Award in Gravity Research Foundation Essay Contest 2008, suggests that we have similarly misunderstood the true nature of gravity because of the way our ideas evolved historically. When seen with the `right side up', the description of gravity becomes remarkably simple, beautiful, and explains features which we never thought needed explanation!

To understand what is involved in this appraoch one could compare the standard, historical, development of gravity with the approach developed by me over the last few years [1]. Historically, Einstein started with the Principle of Equivalence and --- with a few thought experiments --- motivated why gravity should be described by a metric of spacetime. This approach gives the correct backdrop for the equality of inertial and gravitational masses and describes the kinematics of gravity. Unfortunately there is no equally good guiding principle which Einstein could use that leads in a natural fashion to field equations G_ab= κ T_ab which govern the evolution of g_ab (or to the corresponding action principle). So the dynamics of gravity is not backed by a strong guiding principle.

Strange things happen as soon as: (a) we let the metric to be dynamical and (b) allow for arbitrary coordinate transformations or, equivalently, observers on any timelike curve examining physics. Horizons are inevitable in such a theory and they are always observer dependent. This conclusion arises very simply: (i) Principle of equivalence implies that trajectories of light will be acted by gravity. So in any theory which links gravity to spacetime dynamics, we can have nontrivial null surfaces which block information from certain class of observers. (ii) Similarly, one can construct timelike congruences (e.g., uniformly accelerated trajectories) such that all the curves in such a congruence have a horizon. What is more, the horizon is always an observer dependent concept, even when it can be given a purely geometrical definition. For example, the r = 2M surface in Schwarzschild geometry acts operationally as a horizon only for the class of observers who choose to stay at r > 2M and not for the observers falling into the black hole.

Once we have horizons which are inevitable, we get into more trouble. It is an accepted dictum that all observers have a right to describe physics using an effective theory based only on the variables (s)he can access. (This was, of course, the lesson from renormalization group theory. To describe physics at 10 GeV one shouldn't need to know what happens at 10¹⁴ GeV in "good" theories.) This raises the famous question first posed by Wheeler to Bekenstein [2]: What happens if you mix cold and hot tea and pour it down a horizon, erasing all traces of "crime" in increasing the entropy of the world? The answer to such thought experiments demands that horizons should have an entropy which should increase when energy flows across it.

With hindsight, this is obvious. The Schwarschild horizon -- or for that matter any metric which behaves locally like Rindler metric -- has a temperature which can be identified by the Euclidean continuation. If energy dE flows across a hot horizon of temperature T then the ratio dE/T = dS gives the entropy of the horizon. Again, historically, nobody including Wheeler and Bekenstein looked at the Euclidean periodicity in the Euclidean time (in Rindler or Schwarzschild metrics) before Hawking's result came! And the idea of Rindler temperature came after that of black hole temperature! So in summary, the history proceeded as follows:
-----------------------------------------------------------------------------------------
Principle of equivalence ( ~ 1908)

=> Gravity is described by the metric g_ab ( ~ 1908)

? Postulate Einstein's equations without a real guiding principle! (1915)

=> Black hole solutions with horizons (1916) allowing the entropy of hot tea to be hidden ( ~1971)

=> Entropy of black hole horizon (1972)

=> Temperature of black hole horizon (1975)

=> Temperature of the Rindler horizon (1975 -- 1976)
-----------------------------------------------------------------------------------------

There are several peculiar features in the theory for which there is no satisfactory answer in the conventional approach described above and they have to thought of as algebraic accidents. But there is an alternative way of approaching the dynamics of gravity, in which these features emerge as naturally as the equality of inertial and gravitational masses emerges in the geometric description of the kinematics of gravity. These new results also show that the thermodynamic description is far more general than just Einstein's theory and occurs in a wide class of theories in which the metric determines the structure of the light cones and null surfaces exist blocking the information. So instead of the historical path, we can proceed as follows reversing most of the arrows:
-----------------------------------------------------------------------------------------
Principle of equivalence

=> Gravity is described by the metric g_ab

=> Existence of local Rindler frames (LRFs) with a horizon around any event

=>Temperature of the local Rindler horizon H from the Euclidean continuation

=> Virtual displacements of H allow for flow of energy across a hot horizon hiding an entropy dS = dE=T as perceived by a given observer

=> The local horizon must have an entropy, S_grav

=> The dynamics should arise from maximizing the total entropy of horizon (S_grav ) plus matter (S_m) for all LRF's leading to field equations!
-----------------------------------------------------------------------------------------

The procedure uses the local Rindler frame (LRF) around any event P with a local Rindler horizon H. When matter crosses a hot horizon in the LRF -- or, equivalently -- a virtual displacement of the H normal to itself engulfs the matter, some entropy will be lost to the outside observers unless displacing a piece of local Rindler horizon itself costs some entropy S_grav, say. Given the correct expression for S_grav, one can demand that (S_matter + S_grav) should be maximized with respect to all the null vectors which are normals to local patches of null surfaces that can act locally as horizons for a suitable class of observers -- in the spacetime. This puts a constraint on the background spacetime leading to the field equations. To the lowest order, this gives Einstein's equations with calculable corrections [3]. More generally, the resulting field equations are identical to those for Lanczos-Lovelock gravity with a cosmological constant arising as an undetermined integration constant. One can also show, in the general case of Lanczos-Lovelock theory, the on shell value of S_tot gives the correct gravitational entropy, further justifying the original choice. Several peculiar features involving the connection between gravity and thermodynamics is embedded in this approach in a natural fashion. In particular:

♦ There are microscopic degrees of freedom ("atoms of spacetime") which we know nothing about. But just as thermodynamics worked even before we understood atomic structure, we can understand long wavelength gravity arising possibly from a corpuscular spacetime by a thermodynamic approach.

♦ Einstein's equations are essentially thermodynamic identities valid for each and every local Rindler observer [4]. In spacetimes with horizons and high level of symmetry, one can also consider virtual displacements of these horizons (like r_H → r_H + ε) and obviously we will again get TdS = dE + PdV .

♦ If the flow of matter across a horizon costs entropy, the resulting gravitational entropy has to be related to the microscopic degree of freedom associated with the horizon surface. It follows that any dynamical description will require a holographic action with both surface and bulk encoding the same information [5]. For the same reason, the surface term in the action will give the gravitational entropy. Both these features have been investigated in detail by me and my collaborators in the previous years.

Most importantly, this is not just a reformulation of Einstein's theory. Shifting the emphasis from Einstein's field equations to a broader picture of spacetime thermodynamics of horizons leads to a general class of field equations which includes Lanczos-Lovelock gravity. It is now no surprise that Lanczos-Lovelock action is also holographic, is related to entropy and has a thermodynamic interpretation.

References
[1] "Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes", T Padmanabhan, Class. Quan. Grav., 19, 5387, (2002), Abstract [gr-qc/0204019];
"Gravity and the Thermodynamics of Horizons", T. Padmanabhan, Phys. Rept., 406, 49, (2005) [gr-qc/0311036];
"Dark Energy and its Implications for Gravity", T. Padmanabhan, (2008) [arXiv:0807.2356].
[2] This is based on what Wheeler told me in 1985, from his recollection of events; it is also mentioned in his book 'A Journey into Gravity and Space-time', [Scientific American Library, NY, 1990] page 221. I have heard somewhat different versions from other sources.
[3] "Dark Energy and Gravity", T. Padmanabhan, Gen.Rel.Grav., 40, 529-564 (2008). Full Text. [arXiv:0705.2533];
"Entropy of Null Surfaces and Dynamics of Spacetime", T. Padmanabhan, Aseem Paranjape, Phys.Rev. D75 064004 (2007). Abstract. [gr- qc/0701003];
[4] "Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons", D. Kothawala, S. Sarkar, T. Padmanabhan, Phys. Letts, B 652, 338-342 (2007) [gr-qc/0701002];
"Thermodynamic route to field equations in Lanczos-Lovelock gravity", A Paranjape, S Sarkar and T Padmanabhan, Phys. Rev. D 74, 104015 (2006). Abstract.
[5] "Holography of gravitational action functionals", A Mukhopadhyay, T Padmanabhan, Phys. Rev. D74,124023, (2006). Abstract. [arXiv:hep-th/0608120].

Black Holes at the End of the World

Ulf Leonhardt [photo credit: Maud Lang]

[This is an invited article based on an ongoing work led by the author. -- 2Physics.com]

Author: Ulf Leonhardt
Affiliation: School of Physics and Astronomy, University of St Andrews, Scotland

Black Holes are the remainders of supermassive stars that have collapsed under their own weight, but now scientists at the University of St Andrews are using lasers and fibre optics to simulate black holes in the laboratory. They want to test Professor Stephen Hawking’s prediction that black holes are not black after all but glow in the dark.

According to an ancient legend, the Scottish university and golfing town of St Andrews is “the end of the world”. In the 6th century, Saint Regulus, a Greek monk, saw a vision: a dream commanded him to bury the bones of Saint Andrew at the end of the world. So he sailed up the coast of Britain in search of the right place and finally found the perfect spot, St Andrews in fact. Now a small team at the University of St Andrews are using fibre optics and lasers to create artificial black holes at this end of the world. To be absolutely clear: the experiment is perfectly safe. No harm will happen, because these artificial black holes only exist as tiny flashes of light that race through a few inches of optical fibre and are gone when they leave the fibre. The team wants to fulfil a modern type of prophecy, a vision of theoretical physics.

In 1974 Professor Stephen Hawking at Cambridge University published a famous prediction about black holes and quantum physics. Astrophysical black holes are the remainders of collapsed stars. They swallow everything that comes in their way. Their gravity is so strong that not even light can escape. And yet, as Professor Hawking’s flash of insight showed, black holes are not perfectly black; they glow in the dark. However, this Hawking radiation of black holes is so faint that there is probably no chance of ever observing it in space.

Hawking’s theoretical vision has been the stuff of modern legends, because it shows a mysterious connection between various branches of physics, between the physics of the very large, astrophysics, and the physics of the very small, quantum mechanics. According to quantum mechanics, the world is teeming with virtual processes where Nature tries out many things, before some of them turn into reality. At the event horizon of a black hole, virtual light particles are turned into real ones, light is created from nothing, which then radiates into space as Hawking radiation.

The St Andrews team, led by Professor Ulf Leonhardt and Dr Friedrich König, is creating artificial black holes made of light. These creatures resemble real black holes, but they are much smaller (and a lot safer), they have no gravity, but they affect light like their big astrophysical cousins. Professor Leonhardt has been working for a decade on developing and testing ideas of how to engineer optical devices that make Hawking radiation observable. Now he believes he has found the perfect method. In performing and analysing this experiment the scientists hope to understand more about the way Nature creates light quanta at the horizon, something from nothing.

The figure illustrates the principal idea of the experiment. A light pulse in a fibre adds a small contribution to the refractive index, as if an additional piece of glass would be added. This fictitious piece of glass moves with the pulse; so it moves at the speed of light: pulses in fibres behave like materials moving at the speed of light. Imagine that a continuous wave of light follows the pulse, light with a different wavelength. Due to optical dispersion, the velocity of light depends on the wavelength. Suppose that the continuous probe wave is faster than the pulse, but is slowed down by it. The place where the speed of the probe equals the speed of the pulse is the horizon.

Professor Leonhardt put all his eggs in one basket and convinced others to contribute as well. The "start-up capital" for the experiment came from a private donation by Leonhardt Group AG, the corporation of Ulf Leonhardt's cousins Uwe and Helge. Both are businessmen from the Ore Mountains (Erzgebirge) in former East Germany, close to the Bohemian border (at another end of the world). In the less than 20 years after the fall of the Wall they have created quite something from nothing, a multinational corporation. The Leverhulme Trust financed the theory, a charity of Unilever that supports innovative research in the sciences and arts, and that also supported Leonhardt's work on invisibility devices. After the foundations had been laid, the Engineering and Physical Sciences Research Council UK took over. The first results of the team have recently appeared [1], but it will still take time, hard work and further financial support until a legend may become reality at the “end of the world”.

Further information: http://www.st-andrews.ac.uk/~ulf/fibre.html

Reference
[1] "Fiber-Optical Analog of the Event Horizon"
Thomas G. Philbin, Chris Kuklewicz, Scott Robertson, Stephen Hill, Friedrich König, Ulf Leonhardt,
Science 319, 1367 (2008). Abstract Link.

Symmetries, Horizons, and Black Hole Entropy

Author: Steve Carlip

Affiliation: Department of Physics, University of California at Davis

[This is an invited article from Prof. Steve Carlip who received this year's Gravity Research Foundation award for his essay on this topic. The award-winning essay will be published in future issue of General Relativity and Gravitation and International Journal of Modern Physics D.
-- 2Physics.com Team]

Drop a box of hot gas into a black hole. The initial state is gas plus a black hole; the final state is a slightly larger black hole, and nothing else. If the second law of thermodynamics -- which requires that entropy never decrease -- is to hold, the final black hole had better have enough entropy to account for the entropy of the gas it swallowed up.

Thirty-five years ago, Bekenstein used such thought experiments to show that a black hole should have an entropy proportional to the area of its event horizon in Planck units [1]. Soon afterwards,Hawking demonstrated that black holes are, indeed, thermodynamic objects, radiating as black bodies with characteristic temperatures and entropies that match Bekenstein's estimates [2]. In every other thermodynamic system we know, thermal properties reflect the statistical mechanics of underlying microscopic states. Entropy,for example, counts the microstates, while temperature measures their energy. Since the Bekenstein-Hawking entropy involves both Planck's constant and Newton's constant, a statistical mechanical description would have to involve quantum gravity, and might teach us something about the unsolved problem of how to quantize general relativity.

Until fairly recently, no one had a clear idea of the microscopic states responsible for black hole entropy. Today, we suffer the opposite problem: we have many explanations, each describing a different set of states but all agreeing on the final numbers. String theory, for instance, gives us three ways to count black hole states (as excitations of weakly bound branes, as horizonless "fuzzball" geometries, and as states in a dual field theory "at infinity"); loop quantum gravity provides two more; others come from induced gravity, causal set theory, holographic entanglement entropy, and global geometry [3]. None of these approaches is complete, but within its realm of applicability, each seems to work. The new puzzle -- the "problem of universality" -- is to understand why everyone gets the same answer.

One attractive possibility is that a hidden symmetry of classical general relativity controls the thermodynamic properties of black holes. Near the horizon, a black hole looks nearly scale-invariant (technically, conformally invariant) and nearly two-dimensional; quantities such as masses get red-shifted away, as do excitations transverse to the r-t plane. Cardy showed twenty years ago that the thermodynamic properties of a two-dimensional conformal field theory are completely determined by a few parameters that describe its symmetries [4]. Two-dimensional conformal descriptions of matter in a black hole background can be used to derive the spectrum of Hawking radiation [5]; perhaps similar reasoning can be applied to the degrees of freedom of the black hole itself.

To see whether such an explanation makes sense, we must first figure out what it means to ask a question about a black hole in quantum gravity. The uncertainty principle prevents us from simply saying,"A black hole is present." Instead, we must find a way to impose constraints strong enough to ensure the presence of a black hole,but weak enough to be allowed by quantum mechanics. My most recent work has focused on the possibility of introducing such "horizon constraints" as ordinary constraints in the Hamiltonian formulation of general relativity [6]. The results so far are promising: one can obtain the correct Bekenstein-Hawking entropy for a wide class of black holes from the constraints and the symmetry alone. Moreover, there is some evidence of "universality": at least one string theory approach can be understood as a special case of the horizon constraint method, and there are tantalizing hints of a connection with loop quantum gravity. If this explanation is really universal, the horizon constraints should be hidden in other derivations of blackhole entropy as well. We're looking...

A universal explanation of black hole thermodynamics should not, of course, give a complete description of the underlying microstates -- that would ruin its universal character. Still, the horizon constraint method suggests a new way of looking at the degrees of freedom of a black hole. The key point is that the horizon constraints break the fundamental symmetry of general relativity, general covariance (technically, diffeomorphism invariance). As a result, states that would normally be considered equivalent, differing only by a "gauge" transformation, are now physically distinct. This is roughly analogous to the Goldstone mechanism in condensed matter and particle physics, in which a broken symmetry gives rise to new degrees of freedom. In a few cases [7,8], this can be made explicit; it is an open question whether the description works more generally.

The other crucial open question is whether the horizon constraint method can also describe Hawking radiation and other thermodynamic properties of the black hole. To answer, we need to understand how the horizon constraints affect matter near the horizon. This is a hard question, but shouldn't be an impossible one.

References:
[1] J.D. Bekenstein, Phys. Rev. D7 (1973) 2333.
[2] S.W. Hawking, Nature 248 (1974) 30.
[3] For some references, see S. Carlip, J. Phys. Conference Series 67 (2007) 012022, arXiv:gr-qc/0702094.
[4] J.A. Cardy, Nucl. Phys. B270 (1986) 186.
[5] S. Iso, T. Morita, and H. Umetsu, arXiv:hep-th/0701272.
[6] S. Carlip, arXiv:gr-qc/0702107, to appear in Phys. Rev. Lett.
[7] S. Carlip, Class. Quant. Grav. 22 (2005) 3055, arXiv:gr-qc/0501033.
[8] R. Aros, M. Romo, and N. Zamorano, Phys. Rev. D75 (2007) 067501, arXiv:hep-th/0612028.

Here is a Black Hole eating a Star !

This artist's concept shows a supermassive black hole at the center of a remote galaxy digesting the remnants of a star. Image credit: NASA/JPL-Caltech

A giant black hole has been caught red-handed in the act of guzzling a star in a galaxy 4 billion lightyears away in Bootes constellation. This is the first time astronomers have seen the whole process of a black hole eating a star, from its first to nearly final bites.

It is believed that super-massive black holes are located at the core of every galaxy. For example, the Milky Way galaxy in which our solar system resides has a dormant super-massive black hole at its centre. Some blackholes are thought to be more active than others. Active black holes drag surrounding material into them, heating it up and causing it to glow. Dormant black holes, like the one in our Milky Way galaxy, hardly make such a glow, so they are difficult to study.

Such an event like an unsuspecting star wandering too close to a dormant black hole is thought to happen about once every 10,000 years in a typical galaxy. In such a situation, the star gets flattened and stretched apart due to tidal gravitional force, when the black hole's gravity overcomes its own self-gravity. Once a star has been disrupted, a portion of its gaseous body will then be pulled into the black hole and heated up to temperatures that emit X-rays and ultraviolet light.

Scientists used Nasa's Galaxy Evolution Explorer, an orbiting telescope sensitive to two bands of ultraviolet wavelengths, to detect an ultraviolet flare coming from the centre of a remote elliptical galaxy. Scientists said in this case the unfortunate star strayed a bit too close to the black hole deep inside the galaxy, and was mutilated by the force of its gravity. They believe that parts of the star swirled around and then plunged into the black hole, which sent out the bright ultraviolet flare that the satellite detected.

The newfound feeding black hole is thought to be tens of millions times as massive as our sun. Scientists looked at the galaxy in 2003 and there was no ultraviolet light coming from the galaxy at all. And then in 2004, they suddenly saw this very bright source. The only way to explain such a luminous ultraviolet flare is if the black hole swallowed a star.

Additional data from 'Chandra'-- the x-ray telescope in space, the Canada France Hawaii Telescope in Hawaii and the Keck Telescope, also in Hawaii, helped the team chronicle the event in multiple wavelengths over two years.

The results have been published in today's issue of Astrophysical Journal Letters:
"Ultraviolet Detection of the Tidal Disruption of a Star by a Supermassive Black Hole"
S. Gezari, D. C. Martin, B. Milliard, S. Basa, J. P. Halpern, K. Forster, P. G. Friedman, P. Morrissey, S. G. Neff, D. Schiminovich, M. Seibert, T. Small, and T. K. Wyder, The Astrophysical Journal Letters, page L25, volume 653 (Dec 10, 2006). ABSTRACT