The title assertion is proven, and two corollaries are established. First, the topology of every past and future distinguishing spacetime is determined by its causal structure. Second, in every spacetime the path topology of Hawking, King, and McCarthy codes topological, differential, and conformal structure.
Topics
General relativity
REFERENCES
1.
E. H.
Kronheimer
and R.
Penrose
, Proc. Camb. Phil. Soc.
63
, 481
(1967
).2.
S. W.
Hawking
, A. R.
King
, and P. J.
McCarthy
, J. Math. Phys.
17
, 174
(1976
).3.
Proofs of these and subsequent claims can be found in S. W. Hawking and G. F. R. Ellis. The Large Scale Structure of Spacetime (Cambridge U.P., Cambridge, 1973);
R. Penrose, Techniques of Differential Topology in Relativity (SIAM, Philadelphia, 1972).
4.
A proof is given in Hawking, King, and McCarthy (Ref. 2). The theorem is not formulated in exactly this from, but the argument carries over intact.
5.
This version of the theorem is applicable to all temporally orientable spacetimes whether or not a particular temporal orientation is distinguished.
6.
Hawking and Ellis (Ref. 3) prove this in detail in their Lemma 6.2.1.
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© 1977 American Institute of Physics.
1977
American Institute of Physics
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