A Phase Space Approach to Gravitational Enropy

TL;DR

This paper explores a candidate gravitational entropy function based on phase space volume, demonstrating its monotonic increase in various cosmological models and during inflation, while comparing it to Weyl tensor behavior and discussing black hole applications.

Contribution

It introduces a phase space-based gravitational entropy measure and analyzes its properties across different cosmological scenarios and during inflation.

Findings

S increases monotonically in cosmological models

The formalism reproduces the expected entropy during inflation

Black hole applications remain challenging

Abstract

We examine the definition S = ln Omega as a candidate "gravitational entropy" function. We calculate its behavior for gravitationl and density perturbations in closed, open and flat cosmologies and find that in all cases it increases monotonically. Using the formalism to calculate the gravitational entropy produced during inflation gives the canonical answer. We compare the behavior of S with the behavior of the square of the Weyl tensor. Applying the formalism to black holes has proven more problematical.