Naked singularities and quantum gravity

TL;DR

This paper examines the limitations of semiclassical gravity near naked singularities, showing that quantum gravitational effects are necessary to understand the star's ultimate fate, as classical and semiclassical methods break down at Planck scales.

Contribution

It demonstrates that semiclassical approximations fail near naked singularities and highlights the need for quantum gravity to determine the star's final evolution.

Findings

Outgoing quantum flux diverges near the Cauchy horizon

Semiclassical approximation breaks down about one Planck time before singularity formation

Total emitted energy remains finite and about one Planck unit during valid semiclassical period

Abstract

There are known models of spherical gravitational collapse in which the collapse ends in a naked shell-focusing singularity for some initial data. If a massless scalar field is quantized on the classical background provided by such a star, it is found that the outgoing quantum flux of the scalar field diverges in the approach to the Cauchy horizon. We argue that the semiclassical approximation (i.e. quantum field theory on a classical curved background) used in these analyses ceases to be valid about one Planck time before the epoch of naked singularity formation, because by then the curvature in the central region of the star reaches Planck scale. It is shown that during the epoch in which the semiclassical approximation is valid, the total emitted energy is about one Planck unit, and is not divergent. We also argue that back reaction in this model does not become important so long as gravity can be treated classically. It follows that the further evolution of the star will be determined by quantum gravitational effects, and without invoking quantum gravity it is not possible to say whether the star radiates away on a short time scale or settles down into a black hole state.