Gravitational entropy of Hayward black hole

Abstract

We analyze the gravitational entropy defined by the Weyl curvature for the Hayward black hole, which is one of the regular black holes without singularity in the event horizon. Using the definition by the ratio of the Weyl curvature scalar and the Kretschmann scalar as the entropy measure, we evaluate the gravitational entropy on the outer and inner horizons. We derive an expression for the curvature tensor of the Hayward black hole that is as independent as possible of the parameter added to the black hole and give an equation for the entropy measure explicitly independent of that parameter. The gravitational entropy density used in previous studies presents questions from the standpoint of mathematical rigor while we discuss possible improvements in its definition. We compare the results for the Hayward black hole with the analysis for the Reisner–Nordstöm black hole and discuss the effect of singularity resolution on gravitational entropy.