Distinguishing black holes from naked singularities through their accretion disc properties

Abstract

We show that, in principle, a slowly evolving gravitationally collapsing perfect fluid cloud can asymptotically settle to a static spherically symmetric equilibrium configuration with a naked singularity at the center. We consider one such asymptotic final configuration with a finite outer radius, and construct a toy model in which it is matched to a Schwarzschild exterior geometry. We examine the properties of circular orbits in this model. We then investigate observational signatures of a thermal accretion disk in this spacetime, comparing them with the signatures expected for a disk around a black hole of the same mass. Several notable differences emerge. A disk around the naked singularity is much more luminous than one around an equivalent black hole. Also, the disk around the naked singularity has a spectrum with a high frequency power law segment that carries a major fraction of the total luminosity. Thus, at least some naked singularities can, in principle, be distinguished observationally from black holes of the same mass. We discuss possible implications of these results.