Quantum geometrodynamics for black holes and wormholes

Berezin, V. A.; Boyarsky, Alexey; Neronov, A.

doi:10.1103/physrevd.57.1118

Cited by 36 publications

(76 citation statements)

References 5 publications

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“…Several topics are closely related to the subject of this review, but are not included: (1) Various calculations and explanations of the BH entropy [169,355] became a large and rather independent field of research which shows, however, overlaps [165,171] with the general treatment of the dilaton theories presented in this review. We do not cover approaches which imply further physical assumptions which transgress the orthodox application of quantum theory to gravity [34,35,43,24,31].…”

Section: Structure Of This Reviewmentioning

confidence: 99%

“…[427] for a comprehensive review on non-trivial EYM solutions. 34 Throughout this subsection we employ the generally accepted supersymmetry notation with Latin indices from the middle of the alphabet for the holonomic bosonic coordinates x n (denoted "x µ " in the rest of this Report). Greek indices are reserved for the fermionic coordinates θ µ .…”

Section: Dilaton Supergravitymentioning

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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Section: Structure Of This Reviewmentioning

confidence: 99%

Section: Dilaton Supergravitymentioning

confidence: 99%

Dilaton gravity in two dimensions

2002

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“…In particular, the distinctive feature of quantum mechanics of branes is that the differential Schroedinger (or "Wheeler-deWitt") equation for the wave function is replaced by a finite-difference equation [13,15]. This may be a general property of "true" quantum cosmology.…”

mentioning

confidence: 99%

“…[11]. At the classical level σ is integral of the motion, but the change of sign is possible at the quantum level [14,15]. Note that the Hamiltonian constraint Eq.…”

mentioning

confidence: 99%

“…Here we can benefit capitalizing on the fact, that the dynamics of (3+1)-dimensional brane embedded in (4+1)-dimensional bulk, is very similar to the dynamics of self-gravitating shells in conventional (3+1)-dimensional General Relativity, which was studied extensively both at classical [11,12] and quantum levels [13,14,15]. In the present paper we generalize the formalism developed in [15] to the case of the (3+1) dimensional brane universe embedded into (4+1)-dimensional bulk.…”

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confidence: 99%

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Quantum Cosmology of the Brane Universe

2005

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We canonically quantize the dynamics of the brane universe embedded into the five-dimensional Schwarzschild-anti-deSitter bulk space-time. We show that in the brane-world settings the formulation of the quantum cosmology, including the problem of initial conditions, is conceptually more simple than in the 3+1-dimensional case. The Wheeler-deWitt equation is a finite-difference equation. It is exactly solvable in the case of a flat universe and we find the ground state of the system. The closed brane universe can be created as a result of decay of the bulk black hole.Introduction. Quantum effects almost certainly played crucial role in the early universe evolution and in the process of universe creation. Understanding and study of quantum cosmology is important not only from the conceptual point of view, but, hopefully, may provide us with constraints on possible topology of the universe and initial conditions for the inflationary stage [1,2,3]. Appropriate theoretical frameworks which would incorporate all quantum gravitational effects are yet to be constructed, however.String theory, eventually, may provide the consistent approach to the quantum cosmology realm, but the formulation of the string theory on a non-trivial and significantly Lorentzian space time is very complicated and unsolved task ( see for example [4] and references therein). That is why the approaches based on canonical quantization of the Einstein gravity [5] still prove to be more successful in addressing the problems of quantum cosmology. Here one has to adopt a modest approach and restrict consideration to quantum phenomena below the Plank energy scale. Quantizing the universe as a whole one has further resort to the "mini-superspace" modeling [1,2,3,6] in order to get to definite final results (for a recent interesting development see, however, Ref. [7] where effective action for the scale factor was derived integrating out other gravitational degrees of freedom using numerical simulations).Even then, within the "mini-superspace" approach, many conceptual and technical problems remain, such as the problem of ascribing physical meaning to the wave function of the universe [6]. Other important issues are the choice of the boundary conditions which one imposes at the big-bang point (e.g. "no-boundary" [6], "tunneling" [2], etc.) and the problem of unboundedness of the gravitational action (see e.g. [8]).In the present paper we pursue the viewpoint that the presence of extra dimensions can resolve or relax some of these problems. Indeed, in the brane world scenario [9,10], the problem of quantum cosmology (i.e. quantization of gravitational degrees of freedom) is replaced by a much better defined problem of quantum mechanics of the brane (matter degrees of freedom) which moves in the bulk space-time. This has several important consequences. First, one may hope that probabilistic inter-

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Semiclassical S-matrix for black holes

Bezrukov

Levkov

Sibiryakov

2015

J. High Energ. Phys.

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We propose a semiclassical method to calculate S-matrix elements for twostage gravitational transitions involving matter collapse into a black hole and evaporation of the latter. The method consistently incorporates back-reaction of the collapsing and emitted quanta on the metric. We illustrate the method in several toy models describing spherical self-gravitating shells in asymptotically flat and AdS space-times. We find that electrically neutral shells reflect via the above collapse-evaporation process with probability exp(−B), where B is the Bekenstein-Hawking entropy of the intermediate black hole. This is consistent with interpretation of exp(B) as the number of black hole states. The same expression for the probability is obtained in the case of charged shells if one takes into account instability of the Cauchy horizon of the intermediate Reissner-Nordström black hole. Our semiclassical method opens a new systematic approach to the gravitational S-matrix in the non-perturbative regime.

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Quantum geometrodynamics for black holes and wormholes

Cited by 36 publications

References 5 publications

Dilaton gravity in two dimensions

Dilaton gravity in two dimensions

Quantum Cosmology of the Brane Universe

Semiclassical S-matrix for black holes

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