On the Effective Metric of a Planck Star

TL;DR

This paper proposes a modified Hayward metric for non-singular black holes that includes 1-loop quantum corrections and a realistic time delay, addressing physical plausibility and energy condition issues.

Contribution

It introduces a new black hole metric incorporating quantum corrections and a non-trivial time delay, enhancing the physical realism of non-singular black hole models.

Findings

The modified metric includes 1-loop quantum corrections.

It accounts for a non-trivial time delay at the center.

Bounds on time delay are derived based on curvature conditions.

Abstract

Spacetime metrics describing `non-singular' black holes are commonly studied in the literature as effective modification to the Schwarzschild solution that mimic quantum gravity effects removing the central singularity. Here we point out that to be physically plausible, such metrics should also incorporate the 1-loop quantum corrections to the Newton potential and a non-trivial time delay between an observer at infinity and an observer in the regular center. We present a modification of the well-known Hayward metric that features these two properties. We discuss bounds on the maximal time delay imposed by conditions on the curvature, and the consequences for the weak energy condition, in general violated by the large transversal pressures introduced by the time delay.