Black holes and their horizons in semiclassical and modified theories of gravity

TL;DR

This paper reviews the properties of black hole horizons in semiclassical and modified gravity theories, highlighting the implications of assumptions like finite curvature and horizon formation time, and discusses their observational signatures.

Contribution

It identifies only two classes of dynamic solutions for evaporating black holes and white holes under certain assumptions, and analyzes their properties and implications.

Findings

Only two classes of solutions are admissible in spherical symmetry.

Null energy condition is violated near the outer horizon.

Apparent horizons are timelike with singular behavior and negative energy densities.

Abstract

For distant observers black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The first is a consequence of the cosmic censorship conjecture, namely that curvature scalars are finite at apparent horizons. The second is that horizons form in finite asymptotic time (i.e. according to distant observers), a property implicitly assumed in conventional descriptions of black hole formation and evaporation. Taking these as the only requirements within the semiclassical framework, we find that in spherical symmetry only two classes of dynamic solutions are admissible, both describing evaporating black holes and expanding white holes. We review their properties and present the implications. The null energy condition is violated in the vicinity of the outer horizon and satisfied in the vicinity of the inner apparent/anti-trapping horizon. Apparent and anti-trapping horizons are timelike surfaces of intermediately singular behavior, which manifests itself in negative energy density firewalls. These and other properties are also present in axially symmetric solutions. Different generalizations of surface gravity to dynamic spacetimes are discordant and do not match the semiclassical results. We conclude by discussing signatures of these models and implications for the identification of observed ultra-compact objects.