Gravitational entropy in Petrov Type I spacetimes

TL;DR

This paper investigates the application of the gravitational entropy proposal by Clifton, Ellis, and Tavakol to Petrov type I spacetimes, specifically analyzing the effective energy momentum tensors derived from the Bel-Robinson tensor in these contexts.

Contribution

It extends the gravitational entropy framework to Petrov type I spacetimes by analyzing the algebraic decomposition of the Bel-Robinson tensor, using Szekeres models as a test case.

Findings

Derived effective energy momentum tensors for Petrov type I spacetimes.

Applied the framework to Szekeres models of class II.

Addressed limitations of previous applications to types D and N.

Abstract

The gravitational entropy proposal of Clifton, Ellis and Tavakol (CET) is based on an effective energy momentum tensor formed by the algebraic decomposition of the 4th order Bel-Robinson tensor. So far the application of the CET proposal has been limited to spacetimes of Petrov types D and N for which this algebraic decomposition is unique. To address this limitation we examine in detail the effective energy momentum tensors that result from the algebraic decomposition of the Bel-Robinson tensor in Petrov type I spacetimes. As a test case we apply these results to the Szekeres models of class II, a Petrov type I analytic solution.