Spectrum and Statistical Entropy of AdS Black Holes
arXiv:0902.1192 · doi:10.1103/PhysRevD.79.084014
Abstract
Popular approaches to quantum gravity describe black hole microstates differently and apply different statistics to count them. Since the relationship between the approaches is not clear, this obscures the role of statistics in calculating the black hole entropy. We address this issue by discussing the entropy of eternal AdS black holes in dimension four and above within the context of a midisuperspace model. We determine the black hole eigenstates and find that they describe the quantization in half integer units of a certain function of the Arnowitt-Deser-Misner (ADM) mass and the cosmological constant. In the limit of a vanishing cosmological constant (the Schwarzschild limit) the quantized function becomes the horizon area and in the limit of a large cosmological constant it approaches the ADM mass of the black holes. We show that in the Schwarzschild limit the area quatization leads to the Bekenstein-Hawking entropy if Boltzmann statistics are employed. In the limit of a large cosmological constant the Bekenstein-Hawking entropy can be recovered only via Bose statistics. The two limits are separated by a first order phase transition, which seems to suggest a shift from "particle-like" degrees of freedom at large cosmological constant to geometric degrees of freedom as the cosmological constant approaches zero.
14 pages. No figures. Some references added. Version to appear in Phys. Rev. D
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- Quantum Gravitational Collapse in the Lemaitre-Tolman-Bondi Model with a Positive Cosmological Constant
- Tunneling during Quantum Collapse in AdS Spacetime
- Reflection and Transmission at the Apparent Horizon during Gravitational Collapse
- Canonical Partition function of Loop Black Holes
- Decoding infrared imprints of quantum origins of black holes
- Bose Condensation and the BTZ Black Hole
- Signatures of an Emergent Gravity from Black Hole Entropy