Causally symmetric spacetimes are spacetimes with J+(S) isometric to J(S) for some set S. We discuss certain properties of these spacetimes, showing for example that if S is a maximal Cauchy surface with matter everywhere on S, then the spacetime has singularities in both J+(S) and J(S). We also consider totally vicious spacetimes, a class of causally symmetric spacetimes for which I+(p) =I(p) =M for any point p in M. Two different notions of stability in general relativity are discussed, using various types of causally symmetric spacetimes as starting points for perturbations.

1.
R. H.
Gowdy
,
Phys. Rev. Lett.
27
,
826
(
1971
).
2.
A. Einstein, The Meaning of Relativity, fifth ed. (Princeton U.P., Princeton, New Jersey, 1950), p. 107.
3.
C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitatïon (Freeman, San Francisco, 1973), pp. 543, 1181.
4.
It should be mentioned, however, that at present the experimental evidence is against closure. See
J. R.
Gott
,
J. E.
Gunn
,
D. N.
Schramn
, and
B. M.
Tinsley
,
Astrophys. J.
194
,
543
(
1974
).
5.
P. J. E. Peebles, Physical Cosmology (Princeton U.P., Princeton, New Jersey, 1971).
6.
S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Spacetime (Cambridge U.P., Cambridge, 1973).
7.
Ref. 3, p. 535.
8.
The first fruitful use of the concept of time symmetry was made by
D. R.
Brill
in
Ann. Phys.
7
,
466
(
1959
),
and by
H.
Araki
in
Ann. Phys.
7
,
456
(
1959
).These authors use the phrase “time symmetry” to mean the existence of a spacelike hypersurface S with χab = 0andD+(S)≃D(S). (For the precise definition see D. R. Brill, thesis, Princeton University, 1959.)
9.
B. K. Harrison, K. S. Thorne, M. Wakano, and J. A. Wheeler, Gravitation Theory and Gravitational Collapse (University of Chicago Press, Chicago, 1965), p. 13.
10.
A maximal hypersurface is one for which the trace of the extrinsic curvature vanishes: χaa = 0.
11.
D. R.
Brill
and
F. J.
Flaherty
,
Commun. Math. Phys.
50
,
157
(
1976
).
12.
S. W.
Hawking
and
R.
Penrose
,
Proc. R. Soc. A
314
,
529
(
1970
).
13.
R. Penrose, Techniques of Differential Topology in Relativity, Vol. 7 of the Regional Conference Series in Applied Mathematics (SIAM, Philadelphia, 1972).
14.
S. W.
Hawking
and
R. K.
Sachs
,
Commun. Math. Phys.
35
,
287
(
1974
).
15.
S. W.
Hawking
,
Gen. Rel. Grav.
1
,
393
(
1971
).
16.
D. R.
Brill
and
S.
Deser
,
Commun. Math. Phys.
32
,
291
(
1973
).
17.
R.
Geroch
,
J. Math. Phys.
11
,
437
(
1970
).
This content is only available via PDF.
You do not currently have access to this content.