Arrow of time problem in gravitational collapse

TL;DR

The paper analyzes the arrow of time in $N$-dimensional, shear-free radiating gravitational collapse by contrasting a gravitational-entropy (Weyl-based) arrow with the thermodynamic arrow of outgoing radiation. Using two interior models (time-independent and time-modulated lapse) and, later, including charge, it computes curvature scalars and gravitational epoch functions $\\mathcal{P}$ and $\\mathcal{P}_1$ for a higher-dimensional generalized Vaidya exterior and shows that these epoch functions decrease as collapse progresses, indicating the gravitational arrow of time is opposite to the radiative arrow in all dimensions $N\ge 4$. The analysis, including charged interiors and various matching conditions, suggests a local limitation of the Weyl curvature hypothesis and reinforces the idea that shear-free collapse tends toward black-hole end states rather than naked singularities, with the orientation of time arrows remaining dimension-independent. The results underscore the nuanced role of Weyl curvature in local gravitational entropy and its compatibility (or lack thereof) with Penrose's conjecture when applied locally to collapse phenomena.

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.