Critical collapse of a massive scalar field in semi-classical loop quantum gravity

TL;DR

This paper studies how semi-classical loop quantum gravity affects the critical phenomena during the collapse of a massive scalar field, finding that classical behavior largely persists with some differences in black hole mass thresholds.

Contribution

It demonstrates that semi-classical LQG approaches do not significantly alter the classical critical collapse phenomena for a massive scalar field.

Findings

Type II critical phenomena occur at small scalar field mass, matching classical results.

Type I critical phenomena occur at large scalar field mass, with finite minimum black hole mass.

Semi-classical LQG corrections have negligible impact on critical collapse dynamics.

Abstract

We investigate critical phenomena during the gravitational collapse of a massive scalar field under two distinct semi-classical loop quantum gravity (LQG) approaches within spherical symmetry. Numerical simulations reveal that the massive scalar field in both semi-classical frameworks exhibits two distinct types of critical behavior, consistent with the classical scenario. When the scalar field's mass parameter is small, type II critical phenomena emerge, with the resulting echoing periods and critical exponents precisely matching those obtained in general relativity. In contrast, a large mass parameter triggers type I critical phenomena, where the resulting black holes possess a finite minimum mass. These findings suggest that semi-classical corrections from LQG have a negligible impact on the dynamics of critical collapse.