Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts

TL;DR

This paper develops a canonical Hamiltonian framework for two-component spherically symmetric null dust, analyzing gravitational collapse and singularity formation, and identifying complete sets of observables for the system.

Contribution

It extends the canonical formulation to two interacting null dust components, simplifying the mathematics via mass variables and identifying Dirac observables.

Findings

Describes various singularities during collapse.

Constructs a reduced Hamiltonian with gauge fixing.

Identifies complete sets of Dirac observables.

Abstract

The Hamiltonian dynamics of two-component spherically symmetric null dust is studied with regard to the quantum theory of gravitational collapse. The components--the ingoing and outgoing dusts--are assumed to interact only through gravitation. Different kinds of singularities, naked or "clothed", that can form during collapse processes are described. The general canonical formulation of the one-component null-dust dynamics by Bicak and Kuchar is restricted to the spherically symmetric case and used to construct an action for the two components. The transformation from a metric variable to the quasilocal mass is shown to simplify the mathematics. The action is reduced by a choice of gauge and the corresponding true Hamiltonian is written down. Asymptotic coordinates and energy densities of dust shells are shown to form a complete set of Dirac observables. The action of the asymptotic time translation on the observables is defined but it has been calculated explicitly only in the case of one-component dust (Vaidya metric).