Arrow of Time in Gravitational Collapse

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, isotropic 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, measured by the epoch function, is opposite to the thermodynamic arrow of time for all dimensions in such spacetimes. The physical consequences of our results are considered. Our results conform 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 epoch functions to test the Weyl curvature hypothesis, which we have demonstrated in the context of shear-free, pressure-isotropic subclass of radiating spherical collapse for dimension four and beyond.