Hamiltonian evolution and quantization for extremal black holes

Kiefer, Claus; Louko, Jorma

doi:10.1002/(sici)1521-3889(199901)8:1<67::aid-andp67>3.0.co;2-6

Cited by 33 publications

(18 citation statements)

References 35 publications

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“…Here, we use first the expressions in terms of (ε, δ, R), i.e., Eqs. (25), (26), (30), (34), and (38). Then, one finds that the first law Eq.…”

Section: Entropy: the Three Extremal Btz Black Hole Limitsmentioning

confidence: 99%

“…Here, we also have to use the expressions in terms of (ε, δ, R) i.e., Eqs. (25), (26), (30), (34) and (38), and then the first law Eq. (14) can be expressed in terms of the differentials of dǫ, dδ, and dR, as dS(ε, δ, R) = π 2G − Rε √ 1−ε 2 dε + √ 1 − ε 2 dR , which is the same formula as in Case 1.…”

Section: Entropy: the Three Extremal Btz Black Hole Limitsmentioning

confidence: 99%

“…(3), S = A+ 4G , see also Eq. (1), is found through string theory techniques in extremal cases, namely, in (2+1)-dimensional extremal rotating BTZ black holes [19], and in (3+1)-dimensional extremal Reissner-Nordström black holes [20], following the breakthrough worked out in (4+1) dimensions [21,22], see also [23][24][25][26][27][28][29][30][31][32] for further studies on thermodynamics and entropy of extremal black holes. In a sense, Eq.…”

Section: Introductionmentioning

confidence: 99%

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Unified approach to the entropy of an extremal rotating BTZ black hole: Thin shells and horizon limits

2017

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Using a thin shell, the first law of thermodynamics, and a unified approach, we study the thermodymanics and find the entropy of a (2+1)-dimensional extremal rotating Bañados-TeitelbomZanelli (BTZ) black hole. The shell in (2+1) dimensions, i.e., a ring, is taken to be circularly symmetric and rotating, with the inner region being a ground state of the anti-de Sitter (AdS) spacetime and the outer region being the rotating BTZ spacetime. The extremal BTZ rotating black hole can be obtained in three different ways depending on the way the shell approaches its own gravitational or horizon radius. These ways are explicitly worked out. The resulting three cases give that the BTZ black hole entropy is either the Bekenstein-Hawking entropy, S =, or it is an arbitrary function of A+, S = S(A+), where A+ = 2πr+ is the area, i.e., the perimeter, of the event horizon in (2+1) dimensions. We speculate that the entropy of an extremal black hole should obey 0 ≤ S(A+) ≤. We also show that the contributions from the various thermodynamic quantities, namely, the mass, the circular velocity, and the temperature, for the entropy in all three cases are distinct. This study complements the previous studies in thin shell thermodynamics and entropy for BTZ black holes. It also corroborates the results found for a (3+1)-dimensional extremal electrically charged Reissner-Nordström black hole.

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“…Here, we use first the expressions in terms of (ε, δ, R), i.e., Eqs. (25), (26), (30), (34), and (38). Then, one finds that the first law Eq.…”

Section: Entropy: the Three Extremal Btz Black Hole Limitsmentioning

confidence: 99%

Section: Entropy: the Three Extremal Btz Black Hole Limitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Unified approach to the entropy of an extremal rotating BTZ black hole: Thin shells and horizon limits

2017

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“…In the Lovelock case [149] the results suggest that the thermodynamics of five-dimensional Einstein gravity is rather robust with regard to the the introduction of Lovelock terms. Another paper where the Kuchař canonical transformation is used is [133], where the authors consider extremal black holes and how their quantization can be obtained as a limit of non-extremal ones. The obtention of the Bekenstein area quantization in this setting (for Schwarzschild and Reissner-Nordström black holes) is described in [148, 155].…”

Section: Midisuperspaces: Quantizationmentioning

confidence: 99%

Quantization of Midisuperspace Models

Villaseñor

2010

Living Rev. Relativ.

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We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically-symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop-quantum-gravity-inspired methods.

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“…Furthermore, at the equator θ 1 = θ 2 = π/2, the metric (30) is exactly a three-dimensional black hole [17], i.e., 3d anti-de Sitter space with identifications [31]. See [35][36][37][38] for other aspects of higher dimensional CS black holes.…”

Section: Backgroundsmentioning

confidence: 99%

Gravitons and gauge fields in 5d Chern-Simons supergravity

Bañados

2000

Nuclear Physics B - Proceedings Supplements

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Despite the nice geometrical properties of higher dimensional Chern-Simons (CS) supergravity theories these actions suffer from one major drawback, namely, their connection with the real world. After some quick remarks on three-dimensional gravity, we consider five-dimensional CS supergravity and study to what extend this theory reproduces the standard low energy description of gravitons and gauge fields. We point out that if one deforms the CS action by changing the value of the cosmological constant by a small amount (thus breaking the CS symmetry), propagation around AdS becomes non-trivial, asymptotically Schwarzschild-AdS solutions exist, and the gauge field acquires its standard quadratic propagator. This is the written version of an invited Lecture delivered at the QG99 meeting, held in Sardinia, Italy, on Sept. 1999.

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Hamiltonian evolution and quantization for extremal black holes

Cited by 33 publications

References 35 publications

Unified approach to the entropy of an extremal rotating BTZ black hole: Thin shells and horizon limits

Unified approach to the entropy of an extremal rotating BTZ black hole: Thin shells and horizon limits

Quantization of Midisuperspace Models

Gravitons and gauge fields in 5d Chern-Simons supergravity

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