Thermodynamics of warped AdS$_3$ black hole in the brick wall method

TL;DR

This paper calculates the statistical entropy of scalar fields in warped AdS$_3$ black holes using the brick-wall method, revealing that the entropy obeys the area law despite higher-derivative corrections, indicating potential limitations of the method.

Contribution

It demonstrates that the brick-wall method yields an entropy satisfying the area law even with higher-derivative corrections, contrasting with Wald's entropy formula.

Findings

Entropy obeys the area law despite higher-derivative corrections.

Brick-wall method may have limitations in higher-derivative gravity theories.

Scalar field entropy is independent of higher-order derivative terms.

Abstract

The statistical entropy of a scalar field on the warped AdS$_3$ black hole in the cosmological topologically massive gravity is calculated based on the brick-wall method, which is different from the Wald's entropy formula giving the modified area law due to the higher-derivative corrections in that the entropy still satisfies the area law. It means that the entropy for scalar excitations on this background is independent of higher-order derivative terms or the conventional brick wall method has some limitations to take into account the higher-derivative terms.