Comparison theory of Lorentzian distance with applications to spacelike hypersurfaces

Journal Article · Fri May 01 04:00:00 EDT 2009 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3141346· OSTI ID:21304827

Alias, Luis J ^[1]; Hurtado, Ana ^[2]; Palmer, Vicente ^[3]

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1. Departamento de Matematicas, Universidad de Murcia, E-30100 Espinardo, Murcia (Spain)
2. Departamento de Geometria y Topologia, Universidad de Granada, E-18071 Granada (Spain)
3. Departament de Matematiques, Universitat Jaume I, E-12071 Castello (Spain)

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.

• OSTI ID: 21304827
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1122; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
99 GENERAL AND MISCELLANEOUS
BLACK HOLES
COMPARATIVE EVALUATIONS
COSMOLOGY
DISTANCE
GEOMETRY
LORENTZ INVARIANCE
NUMERICAL ANALYSIS
SPACE-TIME