What We Don't Know about BTZ Black Hole Entropy

TL;DR

BTZ black hole entropy remains ill-understood despite several conformal-field-theory derivations. The paper surveys the approaches, emphasizing the lack of consensus on the microscopic degrees of freedom and where excitations reside. It connects BTZ thermodynamics to higher-dimensional black holes with BTZ factors and notes that 3D gravity can be reformulated as a Chern-Simons theory with boundary WZW dynamics. It outlines unresolved problems and suggests directions for developing a first-principles account of the entropy.

Abstract

With the recent discovery that many aspects of black hole thermodynamics can be effectively reduced to problems in three spacetime dimensions, it has become increasingly important to understand the ``statistical mechanics'' of the (2+1)-dimensional black hole of Banados, Teitelboim, and Zanelli (BTZ). Several conformal field theoretic derivations of the BTZ entropy exist, but none is completely satisfactory, and many questions remain open: there is no consensus as to what fields provide the relevant degrees of freedom or where these excitations live. In this paper, I review some of the unresolved problems and suggest avenues for their solution.