Thermodynamics and Evaporation of the 2+1-D Black Hole

TL;DR

This paper investigates the thermodynamics and evaporation processes of 2+1-dimensional black holes in anti-de Sitter space, highlighting different regimes where stable remnants may form and discussing implications for quantum gravity and information loss.

Contribution

It introduces a detailed analysis of black hole thermodynamics in 3D AdS space, identifying relevant mass scales and regimes affecting evaporation and stability, with implications for quantum gravity.

Findings

In the weak coupling regime, black holes may end as stable remnants.

Canonical and microcanonical ensembles are well-defined in AdS space.

Black hole states are more probable than pure radiation states at given temperature or energy.

Abstract

The properties of canonical and microcanonical ensembles of a black hole with thermal radiation and the problem of black hole evaporation in 3-D are studied. In 3-D Einstein-anti-de Sitter gravity we have two relevant mass scales, $m_c=1/G$, and $m_p=(\hbar^2\Lambda/G)^{1/3}$, which are particularly relevant for the evaporation problem. It is argued that in the `weak coupling' regime $\Lambda<(\hbar G)^{-2}$, the end point of an evaporating black hole formed with an initial mass $m_0>m_p$, is likely to be a stable remnant in equilibrium with thermal radiation. The relevance of these results for the information problem and for the issue of back reaction is discussed. In the `strong coupling' regime, $\Lambda>(\hbar G)^{-2}$ a full fledged quantum gravity treatment is required. Since the total energy of thermal states in anti-de Sitter space with reflective boundary conditions at spatial infinity is bounded and conserved, the canonical and microcanonical ensembles are well defined. For a given temperature or energy black hole states are locally stable. In the weak coupling regime black hole states are more probable then pure radiation states.