Global Hyperbolicity and Completeness

Abstract

We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature $K$ are integrable. This last condition is required only for the tracefree part of $K$ if the universe is expanding.

7 pages. Accepted for publication in the Journal of Geometry and Physics. v2: Minor typos corrected

References in corpus (1)

• Future Global in time einsteinian spacetimes with U(1) isometry group

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