Entropy, area, and black hole pairs

Hawking, S. W.; Horowitz, Gary T.; Ross, Simon F.

doi:10.1103/physrevd.51.4302

Cited by 402 publications

(619 citation statements)

References 20 publications

(49 reference statements)

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“…Firstly, it leads to the notion of entropy density [48,32] per unit horizon area. Indeed, when considering local creation processes rather than global ones described by s-waves, the change in area is local [10] in the transverse directions x i ⊥ . This means that a finite and localized set of horizon states are affected by the process.…”

Section: Resultsmentioning

confidence: 99%

“…(32) also applies to the accelerated cases. Indeed even though the area of acceleration horizon might be infinite, the change in the horizon geometry due to a finite change in the matter energy distribution is finite and well defined, see [10] for an explicit computation. In particular, it is local in the transverse directions x i ⊥ when the change in the matter energy distribution is localized.…”

Section: Discussionmentioning

confidence: 99%

“…Using these waves, they derive the black hole emission amplitudes of uninteracting (dilute gas approximation) shells. A similar approach has been used in a Euclidean framework in [9] following the techniques developed in [10]. In this case, the probability for the black hole to emit a particle is expressed in terms of the action S m+g of a self gravitating instanton.…”

Section: Introductionmentioning

confidence: 99%

“…Thus eq. (1) applies to all emission processes in the presence of horizons, including charged and rotating black hole, cosmological and acceleration horizons (in the latter case the horizon area is infinite, but differences are finite and well-defined, see [10,9,19]). …”

Section: Introductionmentioning

confidence: 99%

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How the change in horizon area drives black hole evaporation

2000

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We rephrase the derivation of black hole radiation so as to take into account, at the level of transition amplitudes, the change of the geometry induced by the emission process. This enlarged description reveals that the dynamical variables which govern the emission are the horizon area and its conjugate time variable. Their conjugation is established through the boundary term at the horizon which must be added to the canonical action of general relativity in order to obtain a well defined action principle when the area varies. These coordinates have already been used by Teitelboim and collaborators to compute the partition function of a black hole. We use them to show that the probability to emit a particle is given by e −∆A/4 where ∆A is the decrease in horizon area induced by the emission. This expression improves Hawking result which is governed by a temperature (given by the surface gravity) in that the specific heat of the black hole is no longer neglected. The present derivation of quantum black hole radiation is based on the same principles which are used to derive the first law of classical black hole thermodynamics. Moreover it also applies to quantum processes associated with cosmological or acceleration horizons. These two results indicate that not only black holes but all event horizons possess an entropy which governs processes according to quantum statistical thermodynamics.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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How the change in horizon area drives black hole evaporation

2000

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“…(For application and developing this idea, see [15,16,17].) Recently the interest to the problem of black hole entropy was increased by observation that the entropy of extremal black hole might vanish [18,19].…”

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confidence: 99%

Black Hole Entropy and Physics at Planckian Scales

Frolov¹

1996

String Gravity and Physics at the Planck Energy Scale

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According to the thermodynamical analogy in black hole physics, the entropy of a black hole in the Einstein theory of gravity iswhere A H is the area of a black hole surface and l P = (hG/c 3 ) 1/2 is the Planck length [1,2]. In black hole physics the Bekenstein-Hawking entropy S BH plays essentially the same role as in the usual thermodynamics. In particular it allows to estimate what part of the internal energy of a black hole can be transformed into work. Four laws of black hole physics that form the basis in the thermodynamical analogy were formulated in [3]. According to this analogy the entropy S is defined by the response of the free energy F of the system containing a black hole to the change of its temperature:The generalized second law [1, 2, 4] (see also [5,6,7,8] and references therein) implies that when a black hole is a part of the thermodynamical system the total entropy (i.e. the sum of the entropy of a black hole and the entropy of the surrounding matter) does not decrease. The Euclidean approach [9, 10, 11] provides a natural way to derive black hole thermodynamical properties. Doing a Wick's rotation t → −iτ in the Schwarzschild metric one gets the metric with the Euclidean signature. The corresponding manifold with the Euclidean metric is regular if and only if the imagine time τ is periodic and the period is 2π/κ, where κ is the surface gravity of the black hole. The corresponding *

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Hamiltonian evolution and quantization for extremal black holes

Kiefer

Louko

1999

Ann. Phys.

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We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric Einstein-Maxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary conditions appropriate for extremal black holes only. The Hamil-tonian contains no surface term at the internal infinity, for reasons related to the vanishing of the extremal hole surface gravity, and quantization yields a vanishing black hole entropy. Second, we give a Hamiltonian quantization that incorporates extremal black holes as a limiting case of nonextremal ones, and examine the classical limit in terms of wave packets. The spreading of the packets, even the ones centered about extremal black holes, is consistent with continuity of the entropy in the extremal limit, and thus with the Bekenstein-Hawking entropy even for the extremal holes. The discussion takes place throughout within Lorentz-signature spacetimes.

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Entropy, area, and black hole pairs

Cited by 402 publications

References 20 publications

How the change in horizon area drives black hole evaporation

How the change in horizon area drives black hole evaporation

Black Hole Entropy and Physics at Planckian Scales

Hamiltonian evolution and quantization for extremal black holes

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