Singularity theorems assuming trapped submanifolds of arbitrary dimension

Gregory J. Galloway; José M.M. Senovilla

doi:10.1088/1742-6596/314/1/012092

Singularity theorems assuming trapped submanifolds of arbitrary dimension

Gregory J. Galloway, José M.M. Senovilla

Mathematics

Research output: Contribution to journal › Conference article › peer-review

Abstract

New singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. The timelike or null convergence conditions must be generalized to a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of co-dimension 1, 2 or n. Applications to higher dimensional theories and to the case of trapped circles are briefly mentioned.

Original language	English (US)
Article number	012092
Journal	Journal of Physics: Conference Series
Volume	314
Issue number	1
DOIs	https://doi.org/10.1088/1742-6596/314/1/012092
State	Published - 2011
Event	Spanish Relativity Meeting: Gravity as a Crossroad in Physics, ERE 2010 - Granada, Spain Duration: Sep 6 2010 → Sep 10 2010

ASJC Scopus subject areas

Physics and Astronomy(all)

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abstract = "New singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. The timelike or null convergence conditions must be generalized to a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of co-dimension 1, 2 or n. Applications to higher dimensional theories and to the case of trapped circles are briefly mentioned.",

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