On the Spectrum of the Radiation from a Naked Singularity

In the final stages of collapse, quantum radiation due to particle creation from a naked singularity is expected to be significantly different from black hole radiation. In certain models of collapse it has been shown that, neglecting the back reaction of spacetime, the particle flux on future null infinity grows as the inverse square of the distance from the Cauchy horizon. This is to be contrasted with the flux of radiation from a black hole, which approaches a constant (inversely proportional to the square of its mass) in the neighborhood of its event horizon. The spectrum of black hole radiation is identical to that of a black body at temperature $T = (8\pi M)^{-1}$. We derive the radiation spectrum for a naked singularity formed in the collapse of a marginally bound inhomogeneous dust cloud and show that the spectrum is not black body and admits no simple interpretation.