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.