What We Don't Know about BTZ Black Hole Entropy

TL;DR

This paper reviews unresolved issues in understanding the statistical mechanics of the BTZ black hole, emphasizing the need for a clearer picture of the relevant degrees of freedom and their excitations.

Contribution

It highlights open questions in the conformal field theoretic derivations of BTZ entropy and suggests directions for future research.

Findings

No consensus on the degrees of freedom for BTZ entropy

Unresolved questions about the location of excitations

Review of existing approaches and open problems

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.