Entropy for curvature squared gravity using surface term and auxiliary field

TL;DR

This paper develops a method to compute entropy in curvature squared gravity theories across dimensions by using surface terms and auxiliary fields, unifying results for various models.

Contribution

It introduces an auxiliary tensor field to derive boundary actions, enabling entropy calculations for general curvature squared gravities.

Findings

Reproduces known entropy results for Gauss-Bonnet, NMG, and critical gravity

Provides a unified approach applicable to arbitrary dimensions

Utilizes conserved charges and Virasoro algebra from surface terms

Abstract

We compute the entropies for general curvature squared gravities in arbitrary dimensions using the conserved charge and Virasoro algebra from surface term. We introduce an auxiliary tensor field in order to obtain the boundary action which establish a variational principle. Our results reproduce those in some specific models, that is, the Gauss-Bonnet, new massive gravity (NMG), and critical gravity.