Gravitational entropy in cosmological models

TL;DR

This paper explores potential definitions of gravitational entropy within cosmological models, analyzing specific models like Szekeres and Bianchi type VI_h to evaluate candidate entropy measures.

Contribution

It introduces and assesses a dimensionless scalar function as a candidate for gravitational entropy in cosmological models with isotropic singularities.

Findings

Proposes a dimensionless scalar function as a gravitational entropy candidate

Analyzes Szekeres and Bianchi type VI_h models for entropy behavior

Considers alternative measures like the velocity-dependent Bel-Robinson tensor

Abstract

We discuss whether an appropriately defined dimensionless scalar function might be an acceptable candidate for the gravitational entropy, by explicitly considering Szekeres and Bianchi type VI$_{h}$ models that admit an isotropic singularity. We also briefly discuss other possible gravitational entropy functions, including an appropriate measure of the velocity dependent Bel-Robinson tensor.