Horizon-bound objects: Kerr--Vaidya solutions

TL;DR

This paper analyzes Kerr-Vaidya solutions, a class of dynamical, axially-symmetric spacetimes that model black hole and white hole evolution, identifying conditions for their physical plausibility and extending horizon equivalence concepts.

Contribution

It identifies specific Kerr-Vaidya solutions compatible with finite trapped region formation and extends horizon equivalence to rotating dynamical black holes.

Findings

Kerr-Vaidya solutions can model evaporating black holes and expanding white holes.

Conditions for maintaining asymptotic flatness in dynamical Kerr-Vaidya metrics.

Pathologies such as intermediate singularities in evaporating white hole geometries.

Abstract

Kerr-Vaidya metrics are the simplest dynamical axially-symmetric solutions, all of which violate the null energy condition and thus are consistent with the formation of a trapped region in finite time according to distant observers. We examine different classes of Kerr-Vaidya metrics, and find two which possess spherically-symmetric counterparts that are compatible with the finite formation time of a trapped region. These solutions describe evaporating black holes and expanding white holes. We demonstrate a consistent description of accreting black holes based on the ingoing Kerr--Vaidya metric with increasing mass, and show that the model can be extended to cases where the angular momentum to mass ratio varies. For such metrics we describe conditions on their dynamical evolution required to maintain asymptotic flatness. Pathologies are also identified in the evaporating white hole geometry in the form of an intermediate singularity accessible by timelike observers. We also describe a generalization of the equivalence between Rindler and Schwarzschild horizons to Kerr--Vaidya black holes, and describe the relevant geometric constructions.