Toward a quantization of null dust collapse

Spherically symmetric, null dust clouds, like their timelike 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 Arnowitt-Deser-Misner description by a Kuchar-type canonical transformation. The constraints are linear in the canonical momenta and Dirac's constraint quantization program is implemented. Explicit solutions to the constraints are obtained for both expanding and contracting null dust clouds with arbitrary mass functions