An exploration of the black hole entropy via the Weyl tensor

Abstract

The role of the Weyl tensor (Formula presented.) in black hole thermodynamics is explored by looking at the relation between the scalar invariant (Formula presented.) and the entropy of n-dimensional static black holes. It is found that this invariant can be identified as the entropy density of the gravitational fields for classical 5-dimensional black holes. We calculate the proper volume integrals of (Formula presented.) for the Schwarzschild and Schwarzschild–anti-de Sitter black holes and show that these integrals correctly lead to the Bekenstein–Hawking entropy formulas, only up to some coefficients. ’