Rigid Singularity Theorem in Globally Hyperbolic Spacetimes

Details Rigid Singularity Theorem in Globally Hyperbolic Spacetimes Rigid Singularity Theorem in Globally Hyperbolic Spacetimes

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998tx19.confe..95n&link_type=abstract

Abstracts of the 19th Texas Symposium on Relativistic Astrophysics and Cosmology, held in Paris, France, Dec. 14-18, 1998. Eds.:

Astronomy and Astrophysics

Astrophysics

Scientific paper

We show the following theorem. Let (M,g) be a spacetime which has the following properties: (A) (M,g) is globally hyperbolic. (B) (M,g) satisfies the strong energy condition (RabKaKb >= 0 for all timelike vector Ka). (C) For each closed set C subset S, E^{+}(C) (or E^-(C)) is compact where S is a Cauchy surface. Then (M,g) either is timelike geodesically incomplete or splits into the Lorentzian product of (R, -dt2) and (S,h), where S is a smooth compact spacelike hypersurface and h is the induced metric on S. This result is related to Yau's Lorentzian splitting conjecture.

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