Areas and volumes for null cones

Details Areas and volumes for null cones Areas and volumes for null cones

2010-08-03

arxiv.org/abs/1008.0524v2

Annales Henri Poincare 12:965-985,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, no figures. Typos fixed. One garbled proof corrected. Published version

Scientific paper

10.1007/s00023-011-0090-7

Motivated by recent work of Choquet-Bruhat, Chrusciel, and Martin-Garcia, we prove monotonicity properties and comparison results for the area of slices of the null cone of a point in a Lorentzian manifold. We also prove volume comparison results for subsets of the null cone analogous to the Bishop-Gromov relative volume monotonicity theorem and Guenther's volume comparison theorem. We briefly discuss how these estimates may be used to control the null second fundamental form of slices of the null cone in Ricci-flat Lorentzian four-manifolds with null curvature bounded above.

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