Gravitational Entropy of Black Holes and Wormholes

Abstract

Pure thermodynamical considerations to describe the entropic evolution of the universe seem to violate the Second Law of Thermodynamics. This suggests that the gravitational field itself has entropy. In this paper we expand recent work done by Rudjord, Gr{\O}n and Sigbj{\O}rn where they suggested a method to calculate the gravitational entropy in black holes based on the so-called `Weyl curvature conjecture'. We study the formulation of an estimator for the gravitational entropy of Reissner-Nordstr\"om, Kerr, Kerr-Newman black holes, and a simple case of wormhole. We calculate in each case the entropy for both horizons and the interior entropy density. Then, we analyse whether the functions obtained have the expected behaviour for an appropriate description of the gravitational entropy density.