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Constructing maximal geodesics in strongly causal space-times

Published online by Cambridge University Press:  24 October 2008

John K. Beem  and
Paul E. Ehrlich
John K. Beem
Affiliation:
University of Missouri-Columbia
Paul E. Ehrlich
Affiliation:
University of Missouri-Columbia
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Extract

Let (M, g) be an arbitrary space-time of dimension ≥ 2 and let d = d(g): M × M → ℝ ∪ {∞} (where d(p, q) = 0 for q∉J+(p)) denote the Lorentzian distance function of (M, g). Also let C(M, g) denote the space of Lorentzian metrics for M globally con-formal to g. Here g1 is said to be globally conformal to g if there exists a smooth function Ω: M → (0, ∞) such that g1 = Ωg.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 1 , July 1981 , pp. 183 - 190
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Beem, J. K. and Ehrlich, P. E.Singularities, incompleteness and the Lorentzian distance function. Math. Proc. Cambridge Philos. Soc. 85 (1979), 161–178.CrossRefGoogle Scholar
(2)Beem, J. K. and Ehrlich, P. E.Cut points, conjugate points and Lorentzian comparison theorems. Math. Proc. Cambridge Philos. Soc. 86 (1979), 365–384.CrossRefGoogle Scholar
(3)Beem, J. K. and Ehrlich, P. E.The space-time cut locus. General Relativity and Gravitation, 11 (1979), 89–103.CrossRefGoogle Scholar
(4)Gromoll, D. and Meyer, W.On complete open manifolds of positive curvature. Annals of Math. 90 (1969), 75–90.CrossRefGoogle Scholar
(5)Hawking, S. W. and Ellis, G. F. R.The large-scale structure of space-time. Cambridge University Press, 1973.CrossRefGoogle Scholar
(6)Hawking, S. W. and Penrose, R.The singularities of gravitational collapse and cosmology. Proc. Roy. Soc. London Ser. A 314 (1970), 529–548.Google Scholar
(7)Sachs, R.Gravitational waves in general relativity. VI. The outgoing radiation condition. Proc. Roy. Soc. London Ser. A 264 (1961), 309–338.Google Scholar
(8)Penrose, R.Techniques of differential topology in relativity. SIAM Regional Conference Series in Applied Math. 7 (1972).CrossRefGoogle Scholar