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Global hyperbolicity and completeness

✍ Scribed by Yvonne Choquet-Bruhat; Spiros Cotsakis

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 62 KB
Volume: 43
Category: Article
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(02)00028-1

No coin nor oath required. For personal study only.

✦ Synopsis

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.

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