Lanczos potentials and a definition of gravitational entropy for perturbed FLRW space-times

TL;DR

This paper constructs a Lanczos potential for perturbed FLRW cosmologies, explicitly for radiation models, and proposes a gravitational entropy measure linked to the Weyl tensor's finiteness.

Contribution

It provides a method to explicitly construct Lanczos potentials for perturbed cosmological models and introduces a gravitational entropy definition based on Weyl tensor properties.

Findings

Explicit Lanczos potential for radiation-dominated perturbations

Gravitational entropy finite if initial Weyl tensor is finite

Method applicable to cosmological perturbation analysis

Abstract

We give a prescription for constructing a Lanczos potential for a cosmological model which is a purely gravitational perturbation of a Friedman-Lemaitre-Robertson-Walker space-time. For the radiation equation of state, we find the Lanczos potential explicitly via Fourier transforms. As an application, we follow up a suggestion of Penrose and propose a definition of gravitational entropy for these cosmologies. With this definition, the gravitational entropy initially is finite if and only if the initial Weyl tensor is finite.