Area law of the entropy in the 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 can be expressed by the area law in terms of the brick wall method given by ʼt Hooft. To resolve this discrepancy, 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 even at the critical point.