Marginally Trapped Tubes Generated from Nonlinear Scalar Field Initial Data

We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a selfgravitating 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.