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

Jiri Bicak·Petr Hajicek
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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).

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Jiri Bicak, Petr Hajicek. 2003-08-06. Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts. https://doi.org/10.1103/physrevd.68.104016

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