Classical and quantum LTB model for the non-marginal case

TL;DR

This paper extends the classical and quantum LTB model to the non-marginal case, providing a detailed canonical formalism, boundary term analysis, and exact quantum solutions using lattice regularization.

Contribution

It introduces a comprehensive treatment of the non-marginal LTB model, including classical formalism and exact quantum solutions with lattice regularization.

Findings

Derived classical canonical formalism for non-marginal LTB

Analyzed boundary terms in the action

Obtained exact quantum solutions for specific factor orderings

Abstract

We extend the classical and quantum treatment of the Lemaitre-Tolman-Bondi (LTB) model to the non-marginal case (defined by the fact that the shells of the dust cloud start with a non-vanishing 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.