Non-symmetric trapped surfaces in the Schwarzschild and Vaidya spacetimes

TL;DR

This paper investigates the existence and properties of non-symmetric trapped surfaces in Schwarzschild and Vaidya spacetimes, revealing that such surfaces are common and challenging the reliability of marginally trapped surfaces in dynamical black hole detection.

Contribution

It generalizes the Wald-Iyer construction to Vaidya spacetime and demonstrates the frequent occurrence of non-spherical trapped surfaces outside the standard horizon.

Findings

Non-spherical trapped surfaces extend outside the spherically symmetric horizon in Vaidya spacetime.

MTSs are prevalent in Vaidya spacetime, complicating black hole boundary identification.

Event horizon remains the most probable boundary of the trapped region.

Abstract

Marginally trapped surfaces (MTSs) are commonly used in numerical relativity to locate black holes. For dynamical black holes, it is not known generally if this procedure is sufficiently reliable. Even for Schwarzschild black holes, Wald and Iyer constructed foliations which come arbitrarily close to the singularity but do not contain any MTSs. In this paper, we review the Wald-Iyer construction, discuss some implications for numerical relativity, and generalize to the well known Vaidya spacetime describing spherically symmetric collapse of null dust. In the Vaidya spacetime, we numerically locate non-spherically symmetric trapped surfaces which extend outside the standard spherically symmetric trapping horizon. This shows that MTSs are common in this spacetime and that the event horizon is the most likely candidate for the boundary of the trapped region.