Classical and quantum Lemaître-Tolman-Bondi model for the nonmarginal case

Abstract

We extend the classical and quantum treatment of the Lema\^{\i}tre-Tolman-Bondi (LTB) model to the nonmarginal case (defined by the fact that the shells of the dust cloud start with a nonvanishing velocity at infinity). We present the classical canonical formalism and address with particular care the boundary terms in the action. We give the general relation between dust time and Killing time. Employing a lattice regularization, we then derive and discuss for particular factor orderings exact solutions to all quantum constraints.