Measures of gravitational entropy I. Self-similar spacetimes

TL;DR

This paper investigates whether Weyl curvature can serve as a measure of gravitational entropy in self-similar spacetimes, finding that common scalar measures are unsuitable along homothetic trajectories.

Contribution

It demonstrates that widely used dimensionless scalars of Weyl curvature do not qualify as gravitational entropy measures in self-similar spacetimes.

Findings

Most common Weyl scalars are not suitable as entropy measures.

Symmetry properties impose restrictions on potential gravitational entropy measures.

The study clarifies limitations of Weyl-based entropy proposals in self-similar models.

Abstract

We examine the possibility that the gravitational contribution to the entropy of a system can be identified with some measure of the Weyl curvature. In this paper we consider homothetically self-similar spacetimes. These are believed to play an important role in describing the asymptotic properties of more general models. By exploiting their symmetry properties we are able to impose significant restrictions on measures of the Weyl curvature which could reflect the gravitational entropy of a system. In particular, we are able to show, by way of a more general relation, that the most widely used "dimensionless" scalar is \textit{not} a candidate for this measure along homothetic trajectories.