Entropy of extremal warped black holes

TL;DR

This paper compares different methods of calculating the entropy of extremal warped black holes in topologically massive gravity, confirming their consistency under specific conditions and deriving related formulas.

Contribution

It demonstrates the equivalence of entropy calculations from Wald formalism and entropy function approach for extremal warped black holes.

Findings

Wald and entropy function entropies match when $\alpha=l u$.

The same Cardy formula is obtained under the condition $J_e= l^3 q$.

Results confirm consistency of entropy calculations in this gravity model.

Abstract

We study the entropy of extremal warped black hole obtained from the topologically massive gravity with a negative cosmological constant of $\Lambda=-1/l^2$. We compare the entropy $S_e=\pi \alpha/3G$ from the Wald formalism with $S_w=\pi l u /3G$ from the entropy function approach. These are the same if $\alpha=l u$. Also we obtain the same Cardy formula when $J_e= l^3 q$ with $J_e$ the angular momentum and $q$ the conserved quantity.