BTZ black hole entropy from a Chern–Simons matrix model

Chaney, A.; Lu, Lei; Stern, A.

doi:10.1088/0264-9381/30/23/235016

Cited by 4 publications

(5 citation statements)

References 27 publications

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“…. It is positive for 18) and so the system is stabilized for this range of parameters. The value ω = 0 corresponds to υ/h → +1 or ∞ and hence it is not included in this range.…”

Section: β =mentioning

confidence: 92%

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Matrix model approach to cosmology

Chaney

Stern

2016

Phys. Rev. D

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We perform a systematic search for rotationally invariant cosmological solutions to matrix models, or more specifically the bosonic sector of Lorentzian IKKT-type matrix models, in dimensions d less than ten, specifically d = 3 and d = 5. After taking a continuum (or commutative) limit they yield d − 1 dimensional space-time surfaces, with an attached Poisson structure, which can be associated with closed, open or static cosmologies. For d = 3, we obtain recursion relations from which it is possible to generate rotationally invariant matrix solutions which yield open universes in the continuum limit. Specific examples of matrix solutions have also been found which are associated with closed and static two-dimensional space-times in the continuum limit. The solutions provide for a matrix resolution of cosmological singularities. The commutative limit reveals other desirable features, such as a solution describing a smooth transition from an initial inflation to a noninflationary era. Many of the d = 3 solutions have analogues in higher dimensions. The case of d = 5, in particular, has the potential for yielding realistic four-dimensional cosmologies in the continuum limit. We find four-dimensional de Sitter dS 4 or anti-de Sitter AdS 4 solutions when a totally antisymmetric term is included in the matrix action. A nontrivial Poisson structure is attached to these manifolds which represents the lowest order effect of noncommutativity. For the case of AdS 4 , we find one particlular limit where the lowest order noncommutativity vanishes at the boundary, but not in the interior.

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“…. It is positive for 18) and so the system is stabilized for this range of parameters. The value ω = 0 corresponds to υ/h → +1 or ∞ and hence it is not included in this range.…”

Section: β =mentioning

confidence: 92%

“…Solutions resembling expanding universes were obtained in [9], [12], [14]. In [18] a lower dimensional matrix model was written down from which it was possible to recover the usual BTZ black hole entropy formula. In [19] it was shown how space-time singularities can be resolved in a low-dimensional matrix model.…”

Section: Introductionmentioning

confidence: 99%

Matrix model approach to cosmology

Chaney

Stern

2016

Phys. Rev. D

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“…This setup has been studied in detail before. [24][25][26] The first law of such microstates is written as,…”

Section: Background Geometrymentioning

confidence: 99%

Evaporation of Black Holes in Anti-de Sitter Space-time

Knight¹

2022

Preprint

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We study the thermodynamics of an uncharged, non-rotating BTZ black hole. In addition to the thermal properties, we are interested in the phase transition between two locally thermodynamic stable phases which may arise from different areas of validity for the ads/CFT correspondence. We report on the calculation of entanglement entropies for quantum field theory defined on two dimensional Minkowski space by using its geometric realization as the hyperbolic plane. For free quantum fields in one or more spatial dimensions, we show that a geometric approach reproduces some of the recent results found by studying explicit field correlators. Using this technique, we further explore the geometrical behavior when gravity is turned on and study how it affects thermalization properties such as decoherence times and out-of-equilibrium phase transitions. We show that the microstates for both phases can be described by three macroscopic quantities, thereby allowing us to derive a first order equation for these variables, whereupon they solve this equation at extremality. Superluminal signalling is ruled out if and only if one assumes that no superradiance occurs during evaporation; but it is allowed within the thin membrane paradigm already introduced earlier in this context. Our result holds independent on how long it takes for radiation to escape from near extremal configurations; while there are reasonable expectations regarding this time scale our derivation is completely model-independent.

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“…This setup has been studied in detail before. [25][26][27] The first law of such microstates is written as,…”

Section: Holographic Descriptionmentioning

confidence: 99%

Evaporation of Black Holes in Anti-de Sitter Space-time: A Review

Singh¹

2022

Preprint

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We study the thermodynamics of an uncharged, non-rotating BTZ black hole. In addition to the thermal properties, we are interested in the phase transition between two locally thermodynamic stable phases which may arise from different areas of validity for the ads/CFT correspondence. We report on the calculation of entanglement entropies for quantum field theory defined on two dimensional Minkowski space by using its geometric realization as the hyperbolic plane. For freequantum fields in one or more spatial dimensions, we show that a geometric approach reproducessome of the recent results found by studying explicit field correlators. Using this technique, we further explore the geometrical behavior when gravity is turned on and study how it affects thermalization properties such as decoherence times and out-of-equilibrium phase transitions. We show that the microstates for both phases can be described by three macroscopic quantities, thereby allowing us to derive a first order equation for these variables, whereupon they solve this equation at extremality. Superluminal signalling is ruled out if and only if one assumes that no superradiance occurs during evaporation; but it is allowed within the thin membrane paradigm already introduced earlier in this context. Our result holds independent on how long it takes for radiation to escape from near extremal configurations; while there are reasonable expectations regarding this time scale our derivation is completely model-independent.

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BTZ black hole entropy from a Chern–Simons matrix model

Cited by 4 publications

References 27 publications

Matrix model approach to cosmology

Matrix model approach to cosmology

Evaporation of Black Holes in Anti-de Sitter Space-time

Evaporation of Black Holes in Anti-de Sitter Space-time: A Review

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