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.

23 pages, 3 figures

References in corpus (2)

• The time evolution of marginally trapped surfaces
• Classification of spacelike surfaces in spacetime

Cited by in corpus (6)

• The 1965 Penrose singularity theorem
• The region with trapped surfaces in spherical symmetry, its core, and their boundaries
• Quasi-Local Black Hole Horizons: Recent Advances
• Symmetry and instability of marginally outer trapped surfaces
• Dynamical Horizon Segments and Spacetime Isometries
• Gradient conformal stationarity and the CMC condition in LRS spacetimes