Toward a Quantization of Null Dust Collapse

TL;DR

This paper develops a Hamiltonian framework for null dust collapse, enabling canonical quantization and explicit solutions for various initial conditions, advancing the understanding of black hole and naked singularity formation.

Contribution

It introduces a Kuchař-type canonical transformation for null dust collapse, providing a new approach to quantize and solve the constraints of such systems.

Findings

Explicit solutions for collapsing and expanding null dust clouds.

A linearized constraint structure suitable for quantization.

Framework applicable to arbitrary mass functions.

Abstract

Spherically symmetric, null dust clouds, like their time-like counterparts, may collapse classically into black holes or naked singularities depending on their initial conditions. We consider the Hamiltonian dynamics of the collapse of an arbitrary distribution of null dust, expressed in terms of the physical radius, $R$, the null coordinates, $V$ for a collapsing cloud or $U$ for an expanding cloud, the mass function, $m$, of the null matter, and their conjugate momenta. This description is obtained from the ADM description by a Kucha\v{r}-type canonical transformation. The constraints are linear in the canonical momenta and Dirac's constraint quantization program is implemented. Explicit solutions the constraints are obtained for both expanding and contracting null dust clouds with arbitrary mass functions.