It is shown that causally simple inextendible spacetimes are hole-free, thus confirming the expectation that causal simplicity removes holes from spacetime. This result is optimal in the sense that causal simplicity cannot be weakened to causal continuity. Physically, it means that if there is some partial Cauchy hypersurface which, for some reason, does not fully develop its influence, then there is some discontinuity in the causal relation.
REFERENCES
1.
S. W.
Hawking
and G. F. R.
Ellis
, The Large Scale Structure of Space-Time
(Cambridge University Press
, Cambridge
, 1973
).2.
E.
Minguzzi
and M.
Sánchez
, “The causal hierarchy of spacetimes
,” in Recent Developments in Pseudo-Riemannian Geometry
, edited by H.
Baum
and D.
Alekseevsky
, ESI Lectures in Mathematics and Physics (European Mathematical Society
, Zurich
, 2008
), p. 299
,e-print: arXiv:gr-qc/0609119.
3.
E.
Minguzzi
, “Weak distinction and the optimal definition of causal continuity
,” Class. Quantum Grav.
25
, 075015
(2008
).4.
R.
Geroch
, “Prediction in general relativity
,” in Foundations of Space-Time Theories
, Minnesota Studies in the Philosophy of Science, Vol. VIII
(University of Minnesota
, Minneapolis
, 1977
), p. 81
.5.
J. B.
Manchak
, “Is spacetime hole-free?
” Gen. Relativ. Gravit.
41
, 1639
(2009
).6.
C. J. S.
Clarke
, “Space-time singularities
,” Commun. Math. Phys.
49
, 17
(1976
).7.
J.
Earman
, Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes
(Oxford University Press
, Oxford
, 1995
).8.
C. J. S.
Clarke
, The Analysis of Space-time Singularities
(Cambridge University Press
, Cambridge
, 1993
).9.
S. V.
Krasnikov
, “Even Minkowski spacetime is holed
,” Phys. Rev. D
79
, 124041
(2009
).10.
J. K.
Beem
, “Conformal changes and geodesic completeness
,” Commun. Math. Phys.
49
, 179
(1976
).11.
R.
Penrose
, “A remarkable property of plane waves in general relativity
,” Rev. Mod. Phys.
37
, 215
(1965
).12.
P. E.
Ehrlich
and G. G.
Emch
, “Gravitational waves and causality
,” Rev. Math. Phys.
4
, 163
(1992
).13.
J. K.
Beem
, P. E.
Ehrlich
, and K. L.
Easley
, Global Lorentzian Geometry
(Marcel Dekker
, New York
, 1996
).14.
V. E.
Hubeny
, M.
Rangamani
, and S. F.
Ross
, “Causally pathological spacetimes are physically relevant
,” Int. J. Mod. Phys. D
14
, 2227
(2005
).© 2012 American Institute of Physics.
2012
American Institute of Physics
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