Naked singularity explosion in higher-dimensional dust collapse

Abstract

In the context of the large extra dimensions or TeV-scale gravity, it has been argued that an effective naked singularity, called the visible border of spacetime, would be generated by high-energy particle collisions. Motivated by this interesting possibility, we investigate a particle creation by a naked singularity in general dimensions, adopting a spherically symmetric self-similar dust collapse as the simple model of a naked singularity formation. The power and energy of the particle emission behave in two distinct ways depending on a parameter in the model. In a generic case, the emission power is proportional to the quadratic inverse of the remaining time to the Cauchy horizon, which has been known for the four-dimensional case in the literature. On the other hand, in a degenerate case the emission power is proportional to the quartic inverse of the remaining time to the Cauchy horizon, and depends on the total mass of a dust fluid in spite that the central region of the collapse is scale-free due to the self-similarity. In the both cases, within a test-field approximation the energy radiated before any quantum gravitational effect dominates amounts to TeV. This suggests that a backreaction is not ignorable in the TeV-scale gravity context, in contrast to the similar phenomena in stellar collapse.