Entropy for Asymptotically AdS_3 Black Holes

TL;DR

This paper extends Strominger's method for deriving BTZ black hole entropy to a broader class of asymptotically AdS_3 black holes, confirming the universality of the entropy formula in these cases.

Contribution

The paper demonstrates that Strominger's approach applies to various asymptotically AdS_3 black holes, clarifying which solutions are truly asymptotically AdS_3 and their entropy relations.

Findings

Entropy formulas match Cardy's formula for truly asymptotic AdS_3 solutions.

Some solutions approaching AdS_3 do not have the expected entropy form.

The method is consistent with all known asymptotically AdS_3 black hole solutions.

Abstract

We propose that Strominger's method to derive the BTZ black hole entropy is in fact applicable to other asymptotically AdS_3 black holes and gives the correct functional form of entropies. We discuss various solutions in the Einstein-Maxwell theory, dilaton gravity, Einstein-scalar theories, and Einstein-Maxwell-dilaton theory. In some cases, solutions approach AdS_3 asymptotically, but their entropies do not have the form of Cardy's formula. However, it turns out that they are actually not "asymptotically $AdS_3$" solutions. On the other hand, for truly asymptotically AdS_3 solutions, their entropies have the form of Cardy's formula. In this sense, all known solutions are consistent with our proposal.