Semiclassical black holes and horizon singularities

TL;DR

This paper explores solutions to semiclassical Einstein equations in spherical symmetry, revealing conditions for black hole and white hole formation, horizon properties, and the stability of regular black hole models.

Contribution

It reviews the properties of semiclassical black hole solutions, identifies the only consistent formation scenario, and discusses horizon singularities and stability issues of regular black holes.

Findings

Null energy condition violation near Schwarzschild sphere is necessary for real solutions.

Outer horizons are finite in curvature but weakly singular, with a mild firewall.

Dynamic regular black holes are unstable, stability of models needs further study.

Abstract

In spherical symmetry, solutions of the semiclassical Einstein equations belong to one of two possible classes. Both classes contain solutions that -- depending on the dynamic behavior of the horizon -- describe evaporating physical black holes or expanding white holes (trapped/anti-trapped regions that form in finite time of a distant observer). These solutions are real-valued only if the null energy condition (NEC) is violated in the vicinity of the Schwarzschild sphere. We review their properties and describe the only consistent black hole formation scenario. While the curvature scalars are finite on the outer apparent/anti-trapping horizon, it is still a weakly singular surface. This singularity manifests itself in a mild firewall. Near the inner apparent horizon, the NEC is satisfied. Models of static regular black holes are known to be unstable, but since dynamic models of regular black holes are severely constrained by self-consistency requirements, their stability requires further investigation.