Trapped and marginally trapped surfaces in Weyl-distorted Schwarzschild solutions

TL;DR

This paper investigates Weyl-distorted Schwarzschild solutions, revealing that large distortions can cause the horizon to lose its trapped surface properties, challenging certain black hole definitions.

Contribution

It demonstrates that highly distorted Schwarzschild black holes can have horizons that are not marginally trapped, impacting quasilocal black hole criteria.

Findings

Large distortions break the marginally trapped surface condition

Isolated horizons may not be future outer trapping horizons under distortion

Implications for quasilocal black hole definitions are discussed

Abstract

To better understand the allowed range of black hole geometries, we study Weyl-distorted Schwarzschild solutions. They always contain trapped surfaces, a singularity and an isolated horizon and so should be understood to be (geometric) black holes. However we show that for large distortions the isolated horizon is neither a future outer trapping horizon (FOTH) nor even a marginally trapped surface: slices of the horizon cannot be infinitesimally deformed into (outer) trapped surfaces. We consider the implications of this result for popular quasilocal definitions of black holes.