Global Hyperbolicity and Completeness

Details Global Hyperbolicity and Completeness Global Hyperbolicity and Completeness

2002-01-17

arxiv.org/abs/gr-qc/0201057v2

J.Geom.Phys. 43 (2002) 345-350

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1016/S0393-0440(02)00028-1

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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