The non-imprisonment conditions on spacetimes are studied. It is proved that the non-partial imprisonment property implies the distinction property. Moreover, it is proven that feeble distinction, a property which stays between weak distinction and causality, implies non-total imprisonment. As a result the non-imprisonment conditions can be included in the causal ladder of spacetimes. Finally, totally imprisoned causal curves are studied in detail, and results concerning the existence and properties of minimal invariant sets are obtained.
REFERENCES
1.
Beem
, J. K.
, “Conformal changes and geodesic completeness
,” Commun. Math. Phys.
49
, 179
(1976
).2.
Beem
, J. K.
, Ehrlich
, P. E.
, and Easley
, K. L.
, Global Lorentzian Geometry
(Dekker
, New York
, 1996
).3.
4.
5.
Hawking
, S. W.
, “Chronology protection conjecture
,” Phys. Rev. D
46
, 603
(1992
).6.
Hawking
, S. W.
and Ellis
, G. F. R.
, The Large Scale Structure of Space-Time
(Cambridge University Press
, Cambridge
, 1973
).7.
Hawking
, S. W.
and Sachs
, R. K.
, “Causally continuous spacetimes
,” Commun. Math. Phys.
35
, 287
(1974
).8.
Kronheimer
, E. H.
and Penrose
, R.
, “On the structure of causal spaces
,” Proc. Cambridge Philos. Soc.
63
, 482
(1967
).9.
Minguzzi
, E.
, e-print arXiv:0712.3942.10.
Minguzzi
, E.
, “Weak distinction and the optimal definition of causal continuity
,” Class. Quantum Grav.
25, 075015
(2008
).11.
Minguzzi
, E.
and Sánchez
, M.
, The Causal Hierarchy of Spacetimes
, ESI Lectures in Mathematics and Physics
(European Mathematical Society
, Zurich
, 2008
), pp. 299
–358
.12.
Perko
, L.
, Differential Equations and Dynamical Systems
(Springer-Verlag
, New York
, 1991
).13.
Tiglio
, M. H.
, “No time machine construction in open gravity with timelike total energy-momentum
,” Phys. Rev. D
58
, 064018
(1998
).© 2008 American Institute of Physics.
2008
American Institute of Physics
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