Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant

✍ Scribed by Helmut Friedrich

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 954 KB
• Volume: 3
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/0393-0440(86)90004-5

✦ Synopsis

The initial value problem for Einstein ~field equations with positive cosmological constant is analysed where data are prescribed at past conformalinfinity. It is found that the data on past conformalinfinityaregiven,up to arbitrary conformal rescalings, by a freely specifybleRiemannian metric and a trace-free, symmetric ten sorfield of valence two, which satisfies a divergence equation. For each initial data set exists a unique (semi-global) past asymptotically simple solution of Einstein 's equations. The case is discussed where in such a space-time exists a Killing vector field with a time-like trajectory which approaches a point p on conformal infinity. It is shown that in a neighbourhood of the trajectory near p the spade--time is conformally flat.