Revisiting the gravitational "arrow of time"

TL;DR

This paper reexamines Penrose's gravitational arrow of time hypothesis, clarifying misconceptions and analyzing its validity in specific cosmological models, while comparing it to gravitational entropy concepts.

Contribution

It clarifies the validity of the Weyl-curvature hypothesis in certain cosmological solutions and discusses its relation to gravitational entropy formalism.

Findings

Counterexample by Bonnor does not hold in physically viable models.

The heat conduction vector can be interpreted as a peculiar velocity.

Comparison with gravitational entropy formalism highlights similarities and differences.

Abstract

We address a long-standing misperception on the gravitational ``arrow of time'', a proposal by Penrose (also known as the ``Weyl-curvature hypothesis") that associates structure formation along timelike directions in which Weyl-curvature scalars become dominant over Ricci scalars. A counterexample of this hypothesis was found by Bonnor on a class of exact solutions describing heat conducting spheres collapsing in a Vaidya background. We show that this result does not hold in the same class of solutions considered as physically viable near FLRW cosmological models, with the heat conduction vector interpreted as a peculiar velocity field. We also discuss the similarities and differences between the gravitational ``arrow of time'' and the gravitational entropy formalism of Clifton, Ellis and Tavakol.