Quantum Gravitational Collapse in the Lemaitre-Tolman-Bondi Model with a Positive Cosmological Constant

TL;DR

This paper extends the quantum analysis of the Lemaitre-Tolman-Bondi model to include a positive cosmological constant, deriving solutions to the Wheeler-DeWitt equation and exploring implications like Hawking radiation and the presence of two horizons.

Contribution

It provides new solutions and interpretations for the quantum LTB model with positive cosmological constant, highlighting effects of two horizons absent in the zero Lambda case.

Findings

Derived Wheeler-DeWitt solutions for Lambda > 0

Identified the role of two horizons in the quantum model

Connected solutions to Hawking radiation phenomena

Abstract

Previous papers dealt with the quantization of the Lemaitre-Tolman-Bondi (LTB) model for vanishing cosmological constant $\Lambda$. Here we extend the analysis to the case $\Lambda >0$. Our main goal is to present solutions of the Wheeler-DeWitt equation, to give their interpretation, and to derive Hawking radiation from them. We restrict ourselves to a discussion of those points that are different from the $\Lambda=0$-case. These have mainly to do with the occurrence of two horizons.