Quantum Corrected Spherical Collapse: A Phenomenological Framework

TL;DR

This paper introduces a phenomenological framework incorporating quantum gravity corrections into spherically symmetric collapse, resulting in non-singular black hole solutions with two horizons and altered horizon stability.

Contribution

It develops a variational principle-based effective model that ensures energy conservation and Birkhoff's theorem, leading to novel non-singular solutions with specific horizon structures.

Findings

Prevents formation of a central singularity in collapse.

Results in static spacetimes with two horizons.

Shows the null Cauchy horizon becomes a stable, weak singularity.

Abstract

A phenomenological framework is presented for incorporating quantum gravity motivated corrections into the dynamics of spherically symmetric collapse. The effective equations are derived from a variational principle that guarantees energy conservation and the existence of a Birkhoff theorem. The gravitational potential can be chosen as a function of the areal radius to yield specific non-singular static spherically symmetric solutions that generically have two horizons. For a specific choice of potential the effective stress energy tensor violates only the dominant energy condition. The violations are maximum near the inner horizon and die off rapidly. A numerical study of the quantum corrected collapse of a spherically symmetric scalar field in this case reveals that the modified gravitational potential prevents the formation of a central singularity and ultimately yields a static, mostly vacuum, spacetime with two horizons. The matter "piles up" on the inner horizon giving rise to mass inflation at late times. The Cauchy horizon is transformed into a null, weak singularity, but in contrast to Einstein gravity, the absence of a central singularity renders this null singularity stable.