Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes
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Publication:943573
DOI10.4310/ATMP.2008.V12.N4.A5zbMATH Open1149.83015arXiv0704.2889OpenAlexW2042317870MaRDI QIDQ943573
Author name not available (Why is that?)
Publication date: 9 September 2008
Published in: (Search for Journal in Brave)
Abstract: The present work extends our short communication Phys. Rev. Lett. 95, 111102 (2005). For smooth marginally outer trapped surfaces (MOTS) in a smooth spacetime we define stability with respect to variations along arbitrary vectors v normal to the MOTS. After giving some introductory material about linear non self-adjoint elliptic operators, we introduce the stability operator L_v and we characterize stable MOTS in terms of sign conditions on the principal eigenvalue of L_v. The main result shows that given a strictly stable MOTS S contained in one leaf of a given reference foliation in a spacetime, there is an open marginally outer trapped tube (MOTT), adapted to the reference foliation, which contains S. We give conditions under which the MOTT can be completed. Finally, we show that under standard energy conditions on the spacetime, the MOTT must be either locally achronal, spacelike or null.
Full work available at URL: https://arxiv.org/abs/0704.2889
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