2004/12/13 by José M. M. Senovilla, José M M Senovilla, Senovilla, José M M
Mathematics · Physics and Astronomy · #53B25 #53B30 #53B50 #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #gr-qc #math-ph #math.DG #math.MP #msc:53B25 #msc:53B30 #msc:53B50
paper · pdf · doi:10.48550/arxiv.math/0412256
Contribution to the proceedings of the XIII Fall Workshop on Geometry and Physics, (Murcia, Spain, 2004); Introduction added and minor corrections made
openalex publication_date 2004/12/13 · arxiv created 2005/06/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.