Trapped submanifolds in Lorentzian geometry

Details Trapped submanifolds in Lorentzian geometry Trapped submanifolds in Lorentzian geometry

2004-12-13

arxiv.org/abs/math/0412256v2

Mathematics

Differential Geometry

Contribution to the proceedings of the XIII Fall Workshop on Geometry and Physics, (Murcia, Spain, 2004); Introduction added a

Scientific paper

The concept of closed trapped surface is of paramount importance in General Relativity and other gravitational theories. However, it is a purely geometrical object. With the aim of bringing this concept to closer attention by the mathematical community, I introduce the generalized idea of trapped submanifold by using the causal character of the mean curvature vector. Trapped surfaces can thus be easily seen to be generalizations, possible in semi-Riemannian geometry, of the standard concepts of minimal surfaces, maximal hypersurfaces, geodesics, and the like. Selected applications are mentioned.

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