Quantum Radiation from Black Holes and Naked Singularities in Spherical Dust Collapse

TL;DR

This paper investigates the characteristics of Hawking radiation emitted during spherical dust collapse, comparing black hole formation and naked singularity scenarios, and discusses the thermal nature of the radiation in each case.

Contribution

It analyzes the Hawking radiation in collapse scenarios leading to black holes or naked singularities, highlighting differences in radiation spectra and justifying the use of Bogoliubov transforms.

Findings

Hawking radiation spectrum is thermal in both cases.

Temperature of radiation differs when spacetime terminates at the Cauchy horizon.

Naked singularities can produce observable radiation distinct from black holes.

Abstract

A sufficiently massive collapsing star will end its life as a spacetime singularity. The nature of the Hawking radiation emitted during collapse depends critically on whether the star's boundary conditions are such as would lead to the eventual formation of a black hole or, alternatively, to the formation of a naked singularity. This latter possibility is not excluded by the singularity theorems. We discuss the nature of the Hawking radiation emitted in each case. We justify the use of Bogoliubov transforms in the presence of a Cauchy horizon and show that if spacetime is assumed to terminate at the Cauchy horizon, the resulting spectrum is thermal, but with a temperature different from the Hawking temperature.