A Comment on Kerr-CFT and Wald Entropy

TL;DR

This paper examines discrepancies between black hole entropy calculations using Kerr-CFT and Wald formulas, highlighting that they may not always agree, especially in theories with topological terms like Einstein-Gauss-Bonnet gravity.

Contribution

It identifies and analyzes the mismatch between Kerr-CFT and Wald entropy computations in certain diffeomorphism invariant theories, emphasizing the need for better understanding of boundary terms.

Findings

Kerr-CFT and Wald entropy can differ in Einstein-Gauss-Bonnet gravity.

The central charge remains unchanged, but Wald entropy shows a universal correction.

The Kerr-CFT result is argued to be more physically reasonable in this context.

Abstract

We point out that the entropies of black holes in general diffeomorphism invariant theories, computed using the Kerr-CFT correspondence and the Wald formula (as implemented in the entropy function formalism), need not always agree. A simple way to illustrate this is to consider Einstein-Gauss-Bonnet gravity in four dimensions, where the Gauss-Bonnet term is topological. This means that the central charge of Kerr-CFT computed in the Barnich-Brandt-Compere formalism remains the same as in Einstein gravity, while the entropy computed using the entropy function gives a universal correction proportional to the Gauss-Bonnet coupling. We argue that at least in this example, the Kerr-CFT result is the physically reasonable one. The resolution to this discrepancy might lie in a better understanding of boundary terms.