The Statistical Mechanics of the (2+1)-Dimensional Black Hole

TL;DR

The paper proposes that the entropy of the BTZ black hole in 2+1 dimensions arises from horizon-boundary degrees of freedom that become dynamical when gauge invariance is broken by a boundary. By formulating 2+1 gravity as a pair of Chern-Simons theories and deriving a boundary SO(2,1)×SO(2,1) WZW action under apparent-horizon boundary conditions, it identifies a set of microscopic states associated with the horizon. The state counting, via the affine current algebra and a large-k limit that reduces to six bosonic modes, yields an entropy estimate matching the BTZ result after integrating over a horizon parameter. While several technical caveats remain (e.g., representation choices and nonunitarity), the work provides a concrete statistical-mechanical mechanism for black hole entropy in this simplified setting and motivates possible extensions to higher dimensions.

Abstract

The presence of a horizon breaks the gauge invariance of (2+1)-dimensional general relativity, leading to the appearance of new physical states at the horizon. I show that the entropy of the (2+1)-dimensional black hole can be obtained as the logarithm of the number of these microscopic states.