Arrow of time problem in gravitational collapse

TL;DR

This paper explores the arrow of time in higher-dimensional gravitational collapse, revealing that gravitational entropy's arrow opposes thermodynamic time, challenging existing hypotheses and implications for naked singularity avoidance.

Contribution

It demonstrates that in higher dimensions, the gravitational arrow of time opposes the thermodynamic arrow during shear-free collapse, highlighting a fundamental issue with the Weyl curvature hypothesis.

Findings

Gravitational entropy arrow is opposite to thermodynamic arrow in all dimensions.

Avoidance of naked singularities leads to a wrong arrow of time.

Results align with previous shear-free collapse studies.

Abstract

We investigate the arrow of time problem in the context of gravitational collapse of radiating stars in higher dimensions for both neutral and charged matter. The interior spacetime is described by a shear-free spherically symmetric metric filled with a dissipative fluid. The exterior spacetime of the radiating star is taken as the higher dimensional Vaidya metric. We establish that the arrow of time associated with gravitational entropy is opposite to the thermodynamic arrow of time for all dimensions. The physical consequences of our results are considered. Our result conforms with previous studies on shear-free spherical collapse, which suggests, avoidance of the naked singularity as the end state results in a wrong arrow of time, indicating a fundamental problem with the local application of the Weyl curvature hypothesis.