The Weyl curvature conjecture and black hole entropy

TL;DR

This paper explores the Weyl curvature conjecture as a way to describe gravitational entropy, aiming to connect spacetime geometry with black hole and horizon entropy.

Contribution

It investigates the application of the Weyl curvature conjecture to quantify black hole entropy and cosmological horizon entropy.

Findings

Weyl tensor properties align with gravitational entropy expectations

Potential link between Weyl curvature and black hole entropy

Insights into entropy of horizons with cosmological constant

Abstract

The universe today, with structure such as stars, galaxies and black holes, seems to have evolved from a very homogeneous initial state. From this it appears as if the entropy of the universe is decreasing, in violation of the second law of thermodynamics. It has been suggested by Roger Penrose \cite{grossmann:penrose:wcc} that this inconsistency can be solved if one assigns an entropy to the spacetime geometry. He also pointed out that the Weyl tensor has the properties one would expect to find in a description of a gravitational entropy. In this article we make an attempt to use this so-called Weyl curvature conjecture to describe the Hawking-Bekenstein entropy of black holes and the entropy of horizons due to a cosmological constant.