Comparison theory of Lorentzian distance with applications to spacelike hypersurfaces

In this paper we summarize some comparison results for the Lorentzian distance function in spacetimes, with applications to the study of the geometric analysis of the Lorentzian distance on spacelike hypersurfaces. In particular, we will consider spacelike hypersufaces whose image under the immersio...

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Bibliographic Details
Published in:AIP conference proceedings 2009-05, Vol.1122 (1)
Main Authors: Alias, Luis J., Hurtado, Ana, Palmer, Vicente
Format: Article
Language:English
Subjects:
ASTROPHYSICS, COSMOLOGY AND ASTRONOMY
BLACK HOLES
COMPARATIVE EVALUATIONS
COSMOLOGY
DISTANCE
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
GEOMETRY
LORENTZ INVARIANCE
NUMERICAL ANALYSIS
SPACE-TIME
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Summary:In this paper we summarize some comparison results for the Lorentzian distance function in spacetimes, with applications to the study of the geometric analysis of the Lorentzian distance on spacelike hypersurfaces. In particular, we will consider spacelike hypersufaces whose image under the immersion is bounded in the ambient spacetime and derive sharp estimates for the mean curvature of such hypersurfaces under appropriate hypotheses on the curvature of the ambient spacetime. The results in this paper are part of our recent work, where complete details and further related results may be found.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.3141346