Interface of General Relativity, Quantum Physics and Statistical Mechanics: Some Recent Developments

TL;DR

This paper reviews recent advances in black hole thermodynamics, focusing on isolated horizons that generalize event horizons, and discusses their quantum geometry and entropy from a statistical mechanics perspective.

Contribution

It introduces the concept of isolated horizons, extending black hole thermodynamics to more general, non-stationary situations, and explores their quantum properties and entropy.

Findings

Isolated horizons can be located quasi-locally in space-time.

The zeroth and first laws of black hole mechanics extend to isolated horizons.

Quantum geometry of isolated horizons accounts for their entropy.

Abstract

The arena normally used in black holes thermodynamics was recently generalized to incorporate a broad class of physically interesting situations. The key idea is to replace the notion of stationary event horizons by that of `isolated horizons.' Unlike event horizons, isolated horizons can be located in a space-time quasi-locally. Furthermore, they need not be Killing horizons. In particular, a space-time representing a black hole which is itself in equilibrium, but whose exterior contains radiation, admits an isolated horizon. In spite of this generality, the zeroth and first laws of black hole mechanics extend to isolated horizons. Furthermore, by carrying out a systematic, non-perturbative quantization, one can explore the quantum geometry of isolated horizons and account for their entropy from statistical mechanical considerations. After a general introduction to black hole thermodynamics as a whole, these recent developments are briefly summarized.