BTZ Black Hole with Chern-Simons and Higher Derivative Terms

TL;DR

This paper calculates the entropy of BTZ black holes with higher derivative and Chern-Simons terms using Wald's Noether charge method, providing a new approach to understanding black hole thermodynamics in modified gravity theories.

Contribution

It introduces a novel method applying Wald's Noether charge approach to BTZ black holes with higher derivative and Chern-Simons terms, treating the solution as a two-dimensional black hole.

Findings

Entropy computed via Wald's method matches previous results.

Parameters of the black hole are determined by extremizing an entropy function.

The approach offers a new perspective on black hole entropy in modified gravity.

Abstract

The entropy of a BTZ black hole in the presence of gravitational Chern-Simons terms has previously been analyzed using Euclidean action formalism. In this paper we treat the BTZ solution as a two dimensional black hole by regarding the angular coordinate as a compact direction, and use Wald's Noether charge method to calculate the entropy of this black hole in the presence of higher derivative and gravitational Chern-Simons terms. The parameters labelling the black hole solution can be determined by extremizing an entropy function whose value at the extremum gives the entropy of the black hole.