What We Don't Know about BTZ Black Hole 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.

24 pages, LaTeX, no figures; references added, brief discussion of relation to string theory added; to appear in Class. Quant. Grav

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• Microscopic derivation of the Bekenstein-Hawking entropy formula for non-extremal black holes
• Entropy of Three-Dimensional Black Holes in String Theory
• Near Horizon Geometry and Black Holes in Four Dimensions
• Statistical entropy of charged two-dimensional black holes
• Entropy and Conformal Field Theories of AdS_3 Models

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