Causally continuous general relativistic spacetimes are defined and analyzed. In a causally continuous spacetime, the past and future of a local observer behave continuously under small perturbations of the metric or small changes in his location. Causally simple spacetimes are causally continuous; causally continuous spacetimes are causally stable. Possible reasons for taking causal continuity as a basic postulate in macrophysics are briefly discussed.
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Bishop, R.L., Goldberg, S.I.: Tensor analysis on manifolds, New York: MacMillan 1968
Budic, R., Sachs, R. K.: Set causality in general relativity (preprint, 1973)
Carter, B.: Phys. Rev.174, 1559 (1968)
Carter, B.: Gen. Rel. Grav.1, 349 (1971)
Geroch, R.: J. Math. Phys.11, 437 (1970)
Geroch, R., Kronheimer, E.H., Penrose, R.: Proc. Roy. Soc. A327, 545 (1972)
Hawking, S.: Proc. Roy. Soc. A308, 433 (1968)
Hawking, S., Penrose, R.: Proc. Roy. Soc. A314, 529 (1970)
Hawking, S., Ellis, G.F.R.: The large scale structure of space-time. Cambridge University Press, 1973
Kronheimer, E.H., Penrose, R.: Proc. Cambridge Phil. Soc.63, 481 (1967)
Penrose, R.: Proc. Roy. Soc. A284, 159 (1965)
Penrose, R.: The Structure of Spacetime. In: de Witt, C.M., Wheeler, J.A. (Eds.): Batelle recontres. New York: Benjamin, 1968
Penrose, R.: Techniques of differential topology in general relativity. Am. Math. Soc. Colloq. Publ., 1973
Seifert, H.: Gen. Rel. Grav.1, 3, 247 (1971)
Woodhouse, N.M.J.: J. Math. Phys.14, 4, 495 (1973)
Supported by grants from the NSF, SRC, and Guggenheim foundation.
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Hawking, S.W., Sachs, R.K. Causally continuous spacetimes. Commun.Math. Phys. 35, 287–296 (1974). https://doi.org/10.1007/BF01646350
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