Lanczos potentials and a definition of gravitational entropy for perturbed FLRW space-times
arXiv:gr-qc/0702057 · doi:10.1088/0264-9381/24/7/004
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.
16 pages, submitted for publication in Classical and Quantum Gravity