Arrow of time problem in gravitational collapse

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.