Local foliations and optimal regularity of Einstein spacetimes

Details Local foliations and optimal regularity of Einstein spacetimes Local foliations and optimal regularity of Einstein spacetimes

2008-12-30

arxiv.org/abs/0812.5053v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

47 pages

Scientific paper

We investigate the local regularity of pointed spacetimes, that is, time-oriented Lorentzian manifolds in which a point and a future-oriented, unit timelike vector (an observer) are selected. Our main result covers the class of Einstein vacuum spacetimes. Under curvature and injectivity bounds only, we establish the existence of a local coordinate chart defined in a ball with definite size in which the metric coefficients have optimal regularity. The proof is based on quantitative estimates, on one hand, for a constant mean curvature (CMC) foliation by spacelike hypersurfaces defined locally near the observer and, on the other hand, for the metric in local coordinates that are spatially harmonic in each CMC slice. The results and techniques in this paper should be useful in the context of general relativity for investigating the long-time behavior of solutions to the Einstein equations.

Affiliated with

Also associated with

No associations

Rating

Local foliations and optimal regularity of Einstein spacetimes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Local foliations and optimal regularity of Einstein spacetimes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local foliations and optimal regularity of Einstein spacetimes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-117730