Electromagnetic fields in Schwarzschild and Reissner-Nordström geometry: Quantum corrections to the black hole entropy

Cognola, Guido; Lecca, Paola

doi:10.1103/physrevd.57.1108

Cited by 84 publications

(46 citation statements)

References 33 publications

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“…We call these modes "physical modes II". Physical modes I and II obtained here (and restricted to four dimensions) are identical with those in the A 0 = 0 gauge [8].…”

Section: Gupta-bleuler Quantization In a Modified Feynman Gaugesupporting

confidence: 53%

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Erratum: Quantization of the electromagnetic field outside static black holes and its application to low-energy phenomena [Phys. Rev. D63, 124008 (2001)]

Crispino¹,

Higuchi²,

Matsas³

2009

Phys. Rev. D

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We discuss the Gupta-Bleuler quantization of the free electromagnetic field outside static black holes in the Boulware vacuum. We use a gauge which reduces to the Feynman gauge in Minkowski spacetime. We also discuss its relation with gauges used previously. Then we apply the low-energy sector of this field theory to investigate some low-energy phenomena. First, we discuss the response rate of a static charge outside the Schwarzschild black hole in four dimensions. Next, motivated by string physics, we compute the absorption cross sections of low-energy plane waves for the Schwarzschild and extreme Reissner-Nordström black holes in arbitrary dimensions higher than three.

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“…We call these modes "physical modes II". Physical modes I and II obtained here (and restricted to four dimensions) are identical with those in the A 0 = 0 gauge [8].…”

Section: Gupta-bleuler Quantization In a Modified Feynman Gaugesupporting

confidence: 53%

“…(This gauge is closely related to the A 0 = 0 gauge used by Cognola and Lecca [8] and reduces to the Feynman gauge in Minkowski spacetime.) Then, we calculate some low energy quantities in electrodynamics outside spherically symmetric black holes.…”

Section: Introductionmentioning

confidence: 99%

Erratum: Quantization of the electromagnetic field outside static black holes and its application to low-energy phenomena [Phys. Rev. D63, 124008 (2001)]

Crispino¹,

Higuchi²,

Matsas³

2009

Phys. Rev. D

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“…This approach has been very popular in obtaining the leading order to the black hole entropy in different dimensions (for an incomplete list of references, see Refs. [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]). …”

Section: Introductionmentioning

confidence: 99%

Sub-leading contributions to the black hole entropy in the brick wall approach

Sarkar¹,

Shankaranarayanan²,

Sriramkumar³

2009

Proceedings of Black Holes in General Relativity and String Theory — PoS(BHs, GR and Strings)

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The brick wall model is a semiclassical approach to understand the microscopic origin of black hole entropy. In this approach, the black hole geometry is assumed to be a fixed classical background on which matter fields propagate, and the entropy of black holes supposedly arises due to the canonical entropy of matter fields outside the black hole event horizon, evaluated at the Hawking temperature. Apart from certain lower dimensional cases, the density of states of the matter fields around black holes cannot be evaluated exactly. As a result, often, in the brick wall model, the density of states and the resulting canonical entropy of the matter fields are evaluated at the leading order (in terms of @) in the WKB approximation. The success of the approach is reflected by the fact that the Bekenstein-Hawking area law-viz. that the entropy of black holes is equal to one-quarter the area of their event horizon, say, A Hhas been recovered using this model in a variety of black hole spacetimes. In this work, we compute the canonical entropy of a quantum scalar field around static and spherically symmetric black holes through the brick wall approach at the higher orders (in fact, up to the sixth order in @) in the WKB approximation. We explicitly show that the brick wall model generally predicts corrections to the Bekenstein-Hawking entropy in all spacetime dimensions. In four dimensions, we find that the corrections to the BekensteinHawking entropy are of the form ½A n H logA H , while, in six dimensions, the corrections behave as ½A m H þ A n H logA H , where ðm; nÞ < 1. We compare our results with the corrections to the BekensteinHawking entropy that have been obtained through the other approaches in the literature, and discuss the implications.

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“…Especially researchers pay widespread attention to the statistical origin of the black hole entropy. Many methods of calculating entropy have emerged [4][5][6][7][8][9]. One of them is the well-known brick-wall method [7].…”

Section: Introductionmentioning

confidence: 99%

Entropy of Kerr-Newman Black Hole to All Orders in the Planck Length

Zhao

Zhang

et al. 2008

Int J Theor Phys

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Using the quantum statistical method, the difficulty of solving the wave equation on the background of the black hole is avoided. We directly solve the partition functions of Bose and Fermi field on the background of an axisymmetric Kerr-Newman black hole using the new equation of state density motivated by the generalized uncertainty principle in the quantum gravity. Then near the black hole horizon, we calculate entropies of Bose and Fermi field between the black hole horizon surface and the hypersurface with the same inherent radiation temperature measured by an observer at an infinite distance. In our results there are not cutoffs and little mass approximation introduced in the conventional brick-wall method. The series expansion of the black hole entropy is obtained. And this series is convergent. It provides a way for studying the quantum statistical entropy of a black hole in a nonspherical symmetric spacetime.

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Electromagnetic fields in Schwarzschild and Reissner-Nordström geometry: Quantum corrections to the black hole entropy

Cited by 84 publications

References 33 publications

Erratum: Quantization of the electromagnetic field outside static black holes and its application to low-energy phenomena [Phys. Rev. D63, 124008 (2001)]

Erratum: Quantization of the electromagnetic field outside static black holes and its application to low-energy phenomena [Phys. Rev. D63, 124008 (2001)]

Sub-leading contributions to the black hole entropy in the brick wall approach

Entropy of Kerr-Newman Black Hole to All Orders in the Planck Length

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