Quantum dust collapse with cosmological constant and methods for constructing conformal diagrams

TL;DR

This paper explores the quantum gravitational collapse of dust with a positive cosmological constant, analyzing the global causal structure via numerical construction of Penrose diagrams, revealing persistent issues with timelike singularities.

Contribution

It introduces a robust numerical method for constructing conformal diagrams in quantum-corrected dust collapse scenarios with cosmological constant.

Findings

Exterior geometry resembles Reissner-Nordström-de Sitter black hole

Presence of cosmological constant does not resolve timelike singularities

Quantum effects are incorporated within loop quantum cosmology framework

Abstract

The loop quantum gravitational collapse of the dust ball in presence of positive cosmological constant is investigated within the Oppenheimer-Snyder collapse scenario. The dust ball interior is described within the framework of loop quantum cosmology, while its exterior geometry is determined by the differentiability of the spacetime metric at the dust ball surface and the assumption of the (vacuum) exterior to be stationary. In order to determine the global causal structure of the investigated spacetime a robust (numerical) method of constructing Penrose-Carter diagrams is built. Unfortunately the presence of cosmological constant does not cure the problems already present in the case of it vanishing -- the exterior geometry resembles that of Reissner-Nordstr\"om-de Sitter black hole, in particular featuring timelike singularities.