Marginally trapped tubes generated from nonlinear scalar field initial data

Details Marginally trapped tubes generated from nonlinear scalar field initial data Marginally trapped tubes generated from nonlinear scalar field initial data

2009-01-14

arxiv.org/abs/0901.1921v2

Commun.Math.Phys.293:589-610,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, 4 figures. Updated to agree with published version; small but important error in the proof of the main theorem fixed

Scientific paper

10.1007/s00220-009-0921-2

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.

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