Area law of the entropy in the critical gravity

TL;DR

This paper reconciles two different approaches to black hole entropy in four-dimensional critical gravity, demonstrating that the entropy follows the area law when relating Euclidean action and brick wall methods.

Contribution

It establishes a semiclassical relation between Euclidean action and brick wall methods, confirming the area law of entropy at the critical point in critical gravity.

Findings

Entropy expressed by the area law at the critical point.

Reconciliation of Euclidean and brick wall methods.

Clarification of black hole entropy in critical gravity.

Abstract

The entropy of the Schwarzschild-anti de Sitter black hole in the recently proposed four-dimensional critical gravity is trivial in the Euclidean action formulation, while it is expressed by the area law in terms of the brick wall method given by 't Hooft. To resolve this issue, we relate the Euclidean action formulation to the brick wall method semiclassically, and show that the entropy of the black hole can be expressed by the area law at the critical point.