Marginally trapped tubes generated from nonlinear scalar field initial data
arXiv:0901.1921 · doi:10.1007/s00220-009-0921-2
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.
25 pages, 4 figures. Updated to agree with published version; small but important error in the proof of the main theorem fixed, outline of proof added in Section 2.5, minor expository changes
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