Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes
By Lars-Erik Andersson, M. Mars, W. Simon. 2007
206 citations recorded by the source corpus.
The present work extends our short communication L. Andersson, M. Mars and W. Simon, Local existence of dynamical and trapping horizons, Phys. Rev. Lett. 95 (2005), 111102. 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 nonself-adjoint elliptic operators, we introduce the stability operator Lv and we characterize stable MOTS in terms of sign conditions on the principal eigenvalue of Lv. The main result shows that given a strictly stable MOTS S0 ⊂ Σ0 in a spacetime with a reference foliation Σt, there is an open marginally outer trapped tube (MOTT), adapted to the reference foliation, which contains S0. 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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/6a8c9f7f0a5ec5c14629e2a590cd8b6920d52028
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Citations in the corpus
- The 1965 Penrose singularity theorem (2014, background): “MOTS have been extensively studied in recent years [4, 5, 7, 50], with relevant results for black holes (in which case they are commonly called “apparent horizons””
- Present status of the Penrose inequality (2009, unknown): “The interested reader is referred to [9], [7], [4], [1], [140], [8], [98], [69], [166], [2], [75], [3] and references therein.”