Cardy Entropy of Charged and Rotating Asymptotically AdS and Lifshitz Solutions with a Generalized Chern-Simons term

TL;DR

This paper demonstrates that a generalized Cardy-like formula accurately reproduces the entropy of charged, rotating black holes in 3D gravity models with AdS and Lifshitz asymptotics, including models with Chern-Simons and dilaton fields.

Contribution

It introduces a generalized Cardy-like formula applicable to diverse 3D gravity solutions with different asymptotics and matter content, extending previous entropy calculations.

Findings

Cardy-like formula reproduces Bekenstein-Hawking entropy for charged rotating black holes.

The formula applies to solutions with AdS and Lifshitz asymptotics.

A generalized formula works across models with Chern-Simons and dilaton fields.

Abstract

We consider a three-dimensional gravity model that includes (non-linear) Maxwell and Chern-Simons-like terms, allowing for the existence of electrically charged rotating black hole solutions with a static electromagnetic potential. We verify that a Cardy-like formula, based not on central charges but on the mass of the uncharged and non-spinning soliton, obtained via a double Wick rotation of the neutral static black hole solution, accurately reproduces the Bekenstein-Hawking entropy. Furthermore, we show that a slight generalization of this model, incorporating a dilatonic field and extra gauge fields, admits charged and rotating black hole solutions with asymptotic Lifshitz behavior. The entropy of these solutions can likewise be derived using the Cardy-like formula, with the Lifshitz-type soliton serving as the ground state. Based on these results, we propose a generalized Cardy-like formula that successfully reproduces the semiclassical entropy in all the studied cases.