Quantizing Gravitational Collapse

TL;DR

This paper explores the canonical quantization of gravitational collapse in specific spacetime models, revealing insights into black hole entropy, Hawking radiation, and potential quantum gravity effects on singularity formation.

Contribution

It introduces a quantization approach using Kuchar variables for the LeMaitre-Tolman-Bondi spacetimes, linking quantum effects to black hole thermodynamics and radiation.

Findings

Mass quantization is demonstrated.

Hawking radiation is derived with quantum corrections.

Near-horizon spectrum becomes non-thermal with quantum effects.

Abstract

I summarize some results obtained from a canonical quantization of gravitational collapse. The quantization is carried out in Kuchar variables on the LeMaitre-Tolman-Bondi family of spacetimes. I show how mass quantization, the black hole entropy and Hawking radiation may be understood in these models. Hawking radiation is obtained in the WKB approximation but the first order quantum gravity correction makes the near-horizon spectrum non-thermal, suggesting that unitarity is preserved. The quantization may be used to study quantum gravity effects in collapse leading to the formation of both covered and naked singularities.