Marginally trapped tubes generated from nonlinear scalar field initial data

TL;DR

This paper proves that under specific smallness and decay conditions, the evolution of certain scalar field initial data in general relativity produces a marginally trapped tube that approaches the black hole's event horizon, indicating stability of this structure.

Contribution

It demonstrates the existence and asymptotic behavior of marginally trapped tubes in the evolution of nonlinear scalar field initial data, extending understanding of black hole horizon stability.

Findings

Existence of a connected, achronal marginally trapped tube asymptotic to the event horizon.

Stability of marginally trapped tubes under small perturbations of Schwarzschild.

Conditions on initial data and potential function for the results to hold.

Abstract

We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a self-gravitating nonlinear scalar field, also called a Higgs field, contains a connected, achronal marginally trapped tube which is asymptotic to the event horizon of the black hole, provided the initial data is sufficiently small and decays like O(r^{-1/2}), and the potential function V is nonnegative with bounded second derivative. This result can be loosely interpreted as a statement about the stability of `nice' asymptotic behavior of marginally trapped tubes under certain small perturbations of Schwarzschild.