Toward a Quantization of Null Dust Collapse

Details Toward a Quantization of Null Dust Collapse Toward a Quantization of Null Dust Collapse

2001-12-11

arxiv.org/abs/gr-qc/0112024v2

Phys.Rev. D65 (2002) 104016

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 2 figures (eps), RevTeX4. The last two sections have been revised and corrected. To appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.65.104016

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.

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