Stability of marginally outer trapped surfaces and symmetries

Abstract

We study properties of stable, strictly stable and locally outermost marginally outer trapped surfaces in spacelike hypersurfaces of spacetimes possessing certain symmetries such as isometries, homotheties and conformal Killings. We first obtain results for general diffeomorphisms in terms of the so-called metric deformation tensor and then particularize to different types of symmetries. In particular, we find restrictions at the surfaces on the vector field generating the symmetry. Some consequences are discussed. As an application we present a result on non-existence of stable marginally outer trapped surfaces in slices of FLRW.

arXiv comment23 pages, 3 figures

References in corpus (10)

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Cited by in corpus (10)

• The 1965 Penrose singularity theorem
• The region with trapped surfaces in spherical symmetry, its core, and their boundaries
• Trapped surfaces
• Stability of MOTS in totally geodesic null horizons
• Quasi-Local Black Hole Horizons: Recent Advances
• Symmetry and instability of marginally outer trapped surfaces
• Where are the trapped surfaces?
• Uniqueness theorems for static spacetimes containing marginally outer trapped surfaces
• Gradient conformal stationarity and the CMC condition in LRS spacetimes
• Dynamical Horizon Segments and Spacetime Isometries