The BTZ black hole spectrum and partition function

TL;DR

This paper analyzes the spectrum of the Lorentzian BTZ black hole conformal field theory, identifying its states and relating its partition function to that of $AdS_3$, enhancing understanding of black hole holography.

Contribution

It provides a detailed harmonic analysis of the BTZ black hole spectrum and proposes a connection to the $AdS_3$ CFT spectrum through partition function comparison.

Findings

Identified a complete set of states for the BTZ black hole CFT.

Rewrote the $AdS_3$ CFT partition function to compare with BTZ spectrum.

Suggested that the BTZ black hole spectrum matches that of $AdS_3$.

Abstract

In this article, we revisit the spectrum of the Lorentzian BTZ black hole conformal field theory. Building on a detailed analysis of geodesics, we identify a complete set of states for the harmonic analysis. We then demonstrate that the CFT spectrum is, plausibly, that of $AdS_3$ by rewriting the partition function of the latter CFT.