Revisiting the gravitational ‘arrow of time’

Abstract Penrose’s gravitational ‘arrow of time’ (also known as the ‘Weyl-curvature hypothesis’) associates structure formation along timelike directions in which Weyl-curvature scalars become dominant over Ricci scalars. A frequently cited counterexample to this proposal was found by Bonnor on a class of exact solutions describing heat conducting spheres collapsing in a Vaidya background. In this work, we show that Bonnor’s conclusion does not extend to the same class of solutions considered as physically viable near FLRW cosmological models without an exterior matching. In this cosmological setting, the heat conduction vector can be reinterpreted as a peculiar velocity field, and the Weyl to Ricci curvature ratio evolves in the direction expected from Penrose’s proposal. We also discuss the similarities and differences between the gravitational ‘arrow of time’ and the gravitational entropy formalism of Clifton, Ellis and Tavakol.