Spectrum and Statistical Entropy of AdS Black Holes

TL;DR

This paper investigates the entropy of AdS black holes across different cosmological constants, revealing how quantum states and statistics influence entropy calculations and indicating a phase transition between particle-like and geometric degrees of freedom.

Contribution

It introduces a midisuperspace model to analyze black hole eigenstates and clarifies the role of statistics in entropy, connecting area quantization to different physical regimes.

Findings

Black hole eigenstates quantize a function of mass and cosmological constant.

Bekenstein-Hawking entropy emerges with Boltzmann statistics in the Schwarzschild limit.

Bose statistics are necessary to recover entropy at large cosmological constant.

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.