Symmetries and gravitational Chern-Simons Lagrangian terms

TL;DR

This paper investigates the effects of adding gravitational Chern-Simons terms to covariant gravity theories, showing that under certain conditions, solutions and black hole entropy remain unaffected, supported by three general theorems.

Contribution

It extends previous results by broadening the class of metrics where Chern-Simons terms do not alter solutions or physical quantities, and proves entropy invariance under metric rescaling.

Findings

Chern-Simons terms do not affect solutions in an enlarged class of metrics.

Black hole entropy remains unchanged with Chern-Simons terms for general horizon topologies.

Entropy contribution from Chern-Simons terms is invariant under local metric rescaling.

Abstract

We consider some general consequences of adding pure gravitational Chern-Simons term to manifestly diff-covariant theories of gravity. Extending the result of a previous paper we enlarge the class of metrics for which the inclusion of a gCS term in the action does not affect solutions and corresponding physical quantities. In the case in which such solutions describe black holes (of general horizon topology) we show that the black hole entropy is also unchanged. We arrive at these conclusions by proving three general theorems and studying their consequences. One of the theorems states that the contribution of the gravitational Chern-Simons to the black hole entropy is invariant under local rescaling of the metric.