Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature

Details Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature

2008-12-14

arxiv.org/abs/0812.2671v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages

Scientific paper

We review recent work on the local geometry and optimal regularity of Lorentzian manifolds with bounded curvature. Our main results provide an estimate of the injectivity radius of an observer, and a local canonical foliations by CMC (Constant Mean Curvature) hypersurfaces, together with spatially harmonic coordinates. In contrast with earlier results based on a global bound for derivatives of the curvature, our method requires only a sup-norm bound on the curvature near the given observer.

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