2 research outputs found
Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts
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).Comment: 15 pages, 3 figures, submitted to Phys. Rev.
Toward a Quantization of Null Dust Collapse
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, , the null coordinates, for a collapsing cloud or for an
expanding cloud, the mass function, , 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.Comment: 10 pages, 2 figures (eps), RevTeX4. The last two sections have been
revised and corrected. To appear in Phys. Rev.