Asymptotic Behavior of Spherically Symmetric Marginally Trapped Tubes

TL;DR

This paper establishes conditions under which a spherically symmetric black hole contains a marginally trapped tube that is asymptotic to the event horizon, without requiring Price law decay, and applies these results to Higgs field spacetimes.

Contribution

It provides new sufficient conditions for the existence and asymptotic behavior of marginally trapped tubes in spherically symmetric black holes, extending previous results without relying on Price law decay.

Findings

Existence of marginally trapped tubes under general stress-energy conditions

Asymptotic approach of these tubes to the event horizon without Price law decay

Application to Higgs field spacetimes with different decay assumptions

Abstract

We give conditions on a general stress-energy tensor T_{\alpha \beta} in a spherically symmetric black hole spacetime which are sufficient to guarantee that the black hole will contain a (spherically symmetric) marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Price law decay per se is not required for this asymptotic result, and in this general setting, such decay only implies that the marginally trapped tube has finite length with respect to the induced metric. We do, however, impose a smallness condition (B1) which one may obtain in practice by imposing decay on the T_{vv} component of the stress-energy tensor. We give two applications of the theorem to self-gravitating Higgs field spacetimes, one using weak Price law decay, the other certain strong smallness and monotonicity assumptions.