Involute, minimal, outer and increasingly trapped surfaces

Abstract

Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped surfaces have positivity of a certain curvature, related to surface gravity. Increasingly (future, respectively past) trapped surfaces generate surfaces which are more trapped in a (future, respectively past) causal variation, with three types: in any such causal variation, along the expansion vector, and in some such causal variation. This suggests a definition of doubly outer trapped surface involving two independent curvatures. This in turn suggests a definition of involute trapped surface. Adding a weaker condition, the eight conditions form an interwoven hierarchy, with four independent relations which assume the null energy condition, and another holding in a special case of symmetric curvature.

8 pages

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Cited by in corpus (3)

• The region with trapped surfaces in spherical symmetry, its core, and their boundaries
• The slicing dependence of non-spherically symmetric quasi-local horizons in Vaidya Spacetimes
• Geometrical inequalities bounding angular momentum and charges in General Relativity