Geodesic completeness in static space-times

✍ Scribed by Dean Allison

• Publisher: Springer
• Year: 1988
• Tongue: English
• Weight: 532 KB
• Volume: 26
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00148016

✦ Synopsis

Let (H,h) be a Riemannian manifold and assume f: H-~ (0, oo) is a smooth function. The Lorentzian warped product (a, b) : x H, -oo ~< a < b ~< oo, with metric ds 2 = (__f 2 dt 2) • h is called a standard static space-time. A study is made of geodesic completeness in standard static space-times. Sufficient conditions on the warping function f: H -~ (0, oo) are obtained for (a,b): x H to be timelike and null geodesically complete. In the timelike ease, the sufficient condition is independent of the completeness of the Riemannian manifold (H, h).