Observational Testability of Kerr bound in X-ray Spectrum of Black-Hole Candidates

Abstract

The specific angular momentum of a Kerr black hole must not be larger than its mass. The observational confirmation of this bound which we call a Kerr bound directly suggests the existence of a black hole. In order to investigate observational testability of this bound by using the X-ray energy spectrum of black hole candidates, we calculate energy spectra for a super-spinning object (or a naked singularity) which is described by a Kerr metric but whose specific angular momentum is larger than its mass, and then compare the spectra of this object with those of a black hole. We assume an optically thick and geometrically thin disc around the super-spinning object and calculate its thermal energy spectrum seen by a distant observer by solving general relativistic radiative transfer equations including usual special and general relativistic effects such as Doppler boosting, gravitational redshift, light bending and frame-dragging. Surprisingly, for a given black hole, we can always find its super-spinning counterpart with its spin $a_*$ in the range $5/3<a_*<8\sqrt{6}/3$ whose observed spectrum is very similar to and practically indistinguishable from that of the black hole. As a result, we conclude that to confirm the Kerr bound we need more than the X-ray thermal spectrum of the black hole candidates.