The principled-parameterized approach to gravitational collapse

TL;DR

This paper applies a principle-based method to modify black-hole spacetimes for gravitational collapse, aiming to incorporate new physics beyond General Relativity while ensuring regularity and analyzing geodesic behavior.

Contribution

It extends the principled-parameterized approach to time-dependent collapsing spacetimes, demonstrating regularization and geodesic completeness in dynamic black-hole models.

Findings

Vaidya spacetime becomes regular with modifications

Null geodesics can be future complete due to the modifications

Violations of null energy condition occur inside the apparent horizon

Abstract

New physics beyond General Relativity impacts black-hole spacetimes. The effects of new physics can be investigated in a largely theory-agnostic way by following the principled-parameterized approach. In this approach, a classical black-hole metric is upgraded by following a set of principles, such as regularity, i.e., the absence of curvature singularities. We expect these principles to hold in many theories beyond General Relativity. In the present paper, we implement this approach for time-dependent spacetimes describing gravitational collapse. We find that the Vaidya spacetime becomes regular through the same modification of the spacetime metric as stationary black-hole spacetimes [1-3]. We investigate null geodesics and find indications that the modification is even sufficient to render null geodesics future complete. Finally, we find that the modification of the spacetime structure results in violations of the null energy condition in a finite region inside the apparent horizon of the black hole that forms. Null geodesics are attracted to the boundary of this region, such that the new-physics effects are shielded from asymptotic observers. An exception occurs, if the classical spacetime has a naked singularity. Then, the upgraded spacetime is singularity-free and null geodesics from the regular core can escape towards asymptotic observers.