Gravitational Chern-Simons Lagrangians and black hole entropy

TL;DR

This paper develops a general method to define black hole entropy in theories with gravitational and gauge Chern-Simons terms, extending Wald's formula to non-covariant actions while maintaining covariance.

Contribution

It introduces a unified procedure to compute black hole entropy with Chern-Simons terms in any odd dimension, addressing covariance issues.

Findings

Derived a modified entropy formula similar to Wald's.

Established covariance of the entropy formula despite non-covariance of the action.

Extended the analysis to mixed gauge-gravitational Chern-Simons terms.

Abstract

We analyze the problem of defining the black hole entropy when Chern-Simons terms are present in the action. Extending previous works, we define a general procedure, valid in any odd dimensions both for purely gravitational CS terms and for mixed gauge-gravitational ones. The final formula is very similar to Wald's original formula valid for covariant actions, with a significant modification. Notwithstanding an apparent violation of covariance we argue that the entropy formula is indeed covariant.