Effective Quantum Gravitational Collapse in Metric Variables: The $\bar{\mu}$ Scheme

TL;DR

This paper develops an effective quantum gravity model for gravitational collapse using metric variables and the $ar{}$ scheme from Loop Quantum Gravity, showing singularity avoidance and a transition from black hole to white hole.

Contribution

It introduces a novel effective theory for gravitational collapse with the $ar{}$ scheme, demonstrating singularity resolution and black hole to white hole transition.

Findings

Singularity is avoided due to negative pressure in the effective model.

Collapse transitions from black hole to white hole at Planckian scales.

Effective theory applies to both flat and spherical models.

Abstract

We study, using the metric variables, how an effective theory for the Oppenheimer-Snyder gravitational collapse can be built with the $\bar{\mu}$ scheme from Loop Quantum Gravity (LQG). The collapse is analyzed for both the flat and spherical models. In both scenarios the effective theory make possible to avoid the formation of the singularity. The source of this is found in the presence of a negative pressure term inside the stress-energy tensor of the gravitational field. This pressure is analyzed and is concluded that the effective polymer model is the reason why the negative pressure appears. A characterization of the solutions for both models is also carried out, showing that the collapse is altered and avoided in favor of a transition from a black hole state to a white hole one, transition that occurs when the collapse has reached a Planckian regime.