Mathematics – Mathematical Physics
Scientific paper
Mar 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cmaph.123...17n&link_type=abstract
Communications In Mathematical Physics, Volume 123, Issue 1, pp.17-52
Mathematics
Mathematical Physics
15
Scientific paper
According to a standard definition of Penrose, a space-time admitting well-defined future and past null infinities I + and I - is asymptotically simple if it has no closed timelike curves, and all its endless null geodesics originate from I - and terminate at I +. The global structure of such space-times has previously been successfully investigated only in the presence of additional constraints. The present paper deals with the general case. It is shown that I + is diffeomorphic to the complement of a point in some contractible open 3-manifold, the strongly causal region I {0/+} of I + is diffeomorphic tomathbb{S}^2 × mathbb{R}, and every compact connected spacelike 2-surface in I + is contained in I {0/+} and is a strong deformation retract of both I {0/+} and I +. Moreover the space-time must be globally hyperbolic with Cauchy surfaces which, subject to the truth of the Poincaré conjecture, are diffeomorphic to ℝ3.
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