Singularity theorems based on trapped submanifolds of arbitrary co-dimension

Gregory J Galloway (1) , José M , M Senovilla (2)

1 Department of Mathematics
2 Fsica Teórica, Universidad del Pas Vasco

Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary codimension . By using the mean curvature vector to characterize trapped submanifolds, a unification of the several possibilities for the boundary conditions in the traditional theorems and their generalization to arbitrary co-dimension is achieved. The classical convergence conditions must be replaced by a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of co-dimension 1, 2 or n.

Mots clés: 04.20.Cv; 04.20.Dw; 04.50.-h; 02.40.Ky

Gregory J Galloway, José M , M Senovilla. Singularity theorems based on trapped submanifolds of arbitrary co-dimension. Classical and Quantum Gravity, 2010, 27 (15), pp.152002. ⟨10.1088/0264-9381/27/15/152002⟩. ⟨hal-00613870⟩