Geometrodynamics of Schwarzschild black holes

Kuchař, Karel

doi:10.1103/physrevd.50.3961

Cited by 351 publications

(823 citation statements)

References 25 publications

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“…(7), in the Wheeler-DeWitt constraint, represented here by eqs. (28) and (30). To first order in γ, the modified propagation is expressed in terms of matrix elements of this Hamiltonian sandwiched by the free wave functions, as usual for first order in the Born series.…”

Section: Discussionmentioning

confidence: 99%

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: Discussionmentioning

confidence: 99%

How the change in horizon area drives black hole evaporation

2000

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“…In certain special cases the isometry group of the D-dimensional metric is such that it allows for a reduction to D 1 = 2. Important examples for D = 4 are toroidal reduction [273,189,178,225,56] and spherical reduction [36,412,33,409,205,324,407,244,276,295,195]. The latter is of special importance, because it covers the Schwarzschild BH.…”

Section: Spherically Reduced Gravitymentioning

confidence: 99%

“…Again, this works only patchwise in general since the determinant of the Poisson-tensor can be singular. At a physical level, the symplectic extension resembles Kuchař's geometrodynamics of the Schwarzschild BHs [276]: one introduces a canonically conjugate variable for the conserved quantity (in Kuchař's scenario on the world-sheet boundary, in the symplectic extension in the bulk of target space).…”

Section: Relation To Poisson-sigma Modelsmentioning

confidence: 99%

“…A more complete canonical analysis can be found in refs. [276,307,295,280,299]. The next step is to supplement the volume action (3.67) by a suitable boundary term.…”

Section: Adm Mass and Quasilocal Energymentioning

confidence: 99%

“…Among those models spherically reduced gravity (SRG), the truncation of D = 4 gravity to its s-wave part, possesses perhaps the most direct physical motivation. One can either treat this system directly in D = 4 and impose spherical symmetry in 1 INTRODUCTION the equations of motion (e.o.m.-s) [276] or impose spherical symmetry already in the action [36,412,33,409,205,324,407,244,276,295,195], thus obtaining a dilaton theory 5 . Classically, both approaches are equivalent.…”

Section: Introductionmentioning

confidence: 99%

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Dilaton gravity in two dimensions

2002

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The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important examples of spherically symmetric Black Holes, together with string inspired models, belong to this class, valuable knowledge can also be gained for these systems in the quantum case. In the last decade new insights regarding the exact quantization of the geometric part of such theories have been obtained. They allow a systematic quantum field theoretical treatment, also in interactions with matter, without explicit introduction of a specific classical background geometry. The present review tries to assemble these results in a coherent manner, putting them at the same time into the perspective of the quite large literature on this subject.

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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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Geometrodynamics of Schwarzschild black holes

Cited by 351 publications

References 25 publications

How the change in horizon area drives black hole evaporation

How the change in horizon area drives black hole evaporation

Dilaton gravity in two dimensions

Hamiltonian evolution and quantization for extremal black holes

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