Toward a midisuperspace quantization of LeMaitre-Tolman-Bondi collapse models - art. no. 104020

LeMaitre-Tolman-Bondi models of spherical dust collapse have been used and continue to be used extensively to study various stellar collapse scenarios . It is by now well known that these models lead to the formation of black holes and naked singularities from regular initial data. The final outcome of the collapse, particularly in the event of naked singularity formation, depends very heavily on quantum effects during the final stages. These quan tum effects cannot generally be treated semiclassically as quantum fluctuat ions of the gravitational field are expected to dominate before the final s tate is reached. We present a canonical reduction of LeMaitre-Tolman-Bondi space-times describing the marginally bound collapse of inhomogeneous dust, in which the physical radius R, the proper time of the collapsing dust tau , and the mass function F are the canonical coordinates R(r), tau (r) and F (r) on the phase space. Dirac's constraint quantization leads to a simple f unctional (Wheeler-DeWitt) equation. The equation is solved and the solutio n can be employed to study some of the effects of quantum gravity during gr avitational collapse with different initial conditions.