  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.
