Aspects of Black Hole Quantum Mechanics and Thermodynamics in 2+1 Dimensions

TL;DR

The paper analyzes the (2+1)-dimensional BTZ black hole in Euclidean quantum gravity using minisuperspace and Chern-Simons formalisms. It identifies the horizon deficit angle and twist as dynamical, canonically conjugate variables, derives the classical partition function yielding the BTZ entropy, and computes the first quantum correction, showing a renormalization of the gravitational constant that is independent of Planck's constant for large black holes. By connecting holonomies, identifications, and CS quantization, the authors propose a statistical-mechanical interpretation rooted in horizon degrees of freedom and topological field theory. They also discuss how these ideas might extend to higher dimensions, suggesting a universal role for conical singularities and horizon dynamics in black hole entropy from a topological perspective.

Abstract

We discuss the quantum mechanics and thermodynamics of the (2+1)-dimensional black hole, using both minisuperspace methods and exact results from Chern-Simons theory. In particular, we evaluate the first quantum correction to the black hole entropy. We show that the dynamical variables of the black hole arise from the possibility of a deficit angle at the (Euclidean) horizon, and briefly speculate as to how they may provide a basis for a statistical picture of black hole thermodynamics.