LETTER: Entropy Using Path Integrals for Quantum Black Hole Models

Obregón, O.; Sabido, M.; Tkach, V. I.

doi:10.1023/a:1010216126590

Cited by 34 publications

(52 citation statements)

References 17 publications

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“…Also Kastrup [24], Mäkelä and Repo [25] and Obregon, Sabido and Tkach [27] obtained exactly the same positive correction. More recently, Major and Setter [23] obtained the correction term log A using a model which is motivated by the formulation of geometry in loop quantum gravity (they also describe the black hole in terms of a grand canonical ensemble).…”

Section: Heuristic Scheme and Logarithmic Correctionssupporting

confidence: 54%

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Algebraic approach to quantum black holes: Logarithmic corrections to black hole entropy

Gour

2002

Phys. Rev. D

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The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As shown previously, for a neutral nonrotating black hole, such eigenvalues must be 2 n -fold degenerate if one constructs the black hole stationary states by means of a pair of creation operators subject to a specific algebra. We show that the algebra of these two building blocks exhibits U (2) ≡ U (1) × SU (2) symmetry, where the area operator generates the U (1) symmetry. The three generators of the SU (2) symmetry represent a global quantum number (hyperspin) of the black hole, and we show that this hyperspin must be zero. As a result, the degeneracy of the n-th area eigenvalue is reduced to 2 n /n 3/2 for large n, and therefore, the logarithmic correction term −3/2 log A should be added to the Bekenstein-Hawking entropy. We also provide a heuristic approach explaining this result, and an evidence for the existence of two building blocks.

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Section: Heuristic Scheme and Logarithmic Correctionssupporting

confidence: 54%

“…(22) 27) because N a + N b = n. Thus, the number of independent states with the same area n and the same J 3 is…”

Section: B Degeneracy In the Hyperspin Representationmentioning

confidence: 99%

Algebraic approach to quantum black holes: Logarithmic corrections to black hole entropy

Gour

2002

Phys. Rev. D

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“…By example, quantum gravity models arising from a Wheeler-DeWitt equation for a black hole [33,34] or those considering loop quantum gravity [26,35,36]. There the terms that modify Newton's law are proportional to inverse powers of the radius R and are relevant for radius very close to the Planck's length.…”

Section: Newton's Modified Gravitymentioning

confidence: 99%

Superstatistics and Gravitation

Obregón

2010

Entropy

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We suggest to consider the spacetime as a non-equilibrium system with a long-term stationary state that possess as a spatio-temporally fluctuating quantity β. These systems can be described by a superposition of several statistics, "superstatistics". We propose a Gamma distribution for f (β) that depends on a parameter p l . By means of it the corresponding entropy is calculated, p l is identified with the probability corresponding to this model. A generalized Newton's law of gravitation is then obtained following the entropic force formulation. We discuss some of the difficulties to try to get an associated theory of gravity.

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“…For related and other approaches, see [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. For other applications of (17), see [31].…”

Section: Thermal Fluctuations and Entropymentioning

confidence: 99%

Anti-de Sitter black holes, perfect fluids and holography

Das¹,

Husain²

2003

Class. Quantum Grav.

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We consider asymptotically anti-de Sitter black holes in d-spacetime dimensions in the thermodynamically stable regime. We show that the Bekenstein-Hawking entropy and its leading order corrections due to thermal fluctuations are reproduced by a weakly interacting fluid of bosons and fermions ('dual gas') in ∆ = α(d − 2) + 1 spacetime dimensions, where the energy-momentum dispersion relation for the constituents of the fluid is assumed to be ǫ = κp α . We examine implications of this result for entropy bounds and the holographic hypothesis.

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LETTER: Entropy Using Path Integrals for Quantum Black Hole Models

Cited by 34 publications

References 17 publications

Algebraic approach to quantum black holes: Logarithmic corrections to black hole entropy

Algebraic approach to quantum black holes: Logarithmic corrections to black hole entropy

Superstatistics and Gravitation

Anti-de Sitter black holes, perfect fluids and holography

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