Where are the BTZ Black Hole Degrees of Freedom?

TL;DR

This paper demonstrates that the dual conformal description of the non-rotating BTZ black hole's degrees of freedom is valid at any spatial location, not just at infinity, aligning with the absence of propagating degrees in 2+1 dimensions.

Contribution

It shows the existence of a dual conformal description at any radius around the BTZ black hole, extending previous results limited to spatial infinity.

Findings

Dual conformal description exists at any radius

Central charge of 3ℓ/2G is recovered

Cardy formula yields Bekenstein-Hawking entropy

Abstract

Previous derivations of the BTZ black hole entropy from a dual conformal description place the degrees of freedom at spatial infinity. Here it is shown for the non-rotating case that a dual conformal description exists at any location around the black hole, a result that has a strong physical appeal considering that in 2+1 dimensions there are no propagating degrees of freedom in the classical theory. Two copies of the central charge of $3\ell/2G$ are recovered, and the microcanonical Cardy formula yields the correct Bekenstein-Hawking entropy.