# 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.

## Key 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.