The global structure of simple space-times |
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Authors: | Richard P A C Newman |
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Institution: | (1) Department of Mathematics, Institute of Advanced Studies, Australian National University, GPO Box 4, 2601 Canberra, A.C.T., Australia |
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Abstract: | According to a standard definition of Penrose, a space-time admitting well-defined future and past null infinitiesI
+ andI
– is asymptotically simple if it has no closed timelike curves, and all its endless null geodesics originate fromI
– and terminate atI
+. 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 thatI
+ is diffeomorphic to the complement of a point in some contractible open 3-manifold, the strongly causal regionI
0
+
ofI
+ is diffeomorphic to
, and every compact connected spacelike 2-surface inI
+ is contained inI
0
+
and is a strong deformation retract of bothI
0
+
andI
+. Moreover the space-time must be globally hyperbolic with Cauchy surfaces which, subject to the truth of the Poincaré conjecture, are diffeomorphic to 3. |
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Keywords: | |
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