Notes on black holes and three dimensional gravity

TL;DR

This paper provides an accessible overview of black holes and 2+1 dimensional quantum gravity, including classical, semiclassical, and quantum aspects, with emphasis on the Chern-Simons formulation and related algebraic structures.

Contribution

It offers a simplified, lecture-based review of key results in 2+1 quantum gravity, including the Chern-Simons approach and asymptotic symmetries, serving as a complementary resource.

Findings

Review of classical and semiclassical black hole properties

Explanation of the Chern-Simons formulation of 2+1 gravity

Discussion of the asymptotic algebra of Brown and Henneaux

Abstract

These notes are the written version of two lectures delivered at the VIII Mexican School on Particles and Fields on November 1998. The level of the notes is basic assuming only some knowledge on Statistical Mechanics, General Relativity and Yang-Mills theory. After a brief introduction to the classical and semiclassical aspects of black holes, we review some relevant results on 2+1 quantum gravity. These include the Chern-Simons formulation and its affine Kac-Moody algebra, the asymptotic algebra of Brown and Henneaux, and the statistical mechanics description of 2+1 black holes. Hopefully, this contribution will be complementary with the review paper hep-th/9901148 by the same author, and perhaps, a shortcut to some recent developments in three dimensional gravity.