Compact Lorentzian manifolds without closed nonspacelike geodesics

Galloway, Gregory J.

doi:10.1090/S0002-9939-1986-0848888-7

Compact Lorentzian manifolds without closed nonspacelike geodesics
HTML articles powered by AMS MathViewer

by Gregory J. Galloway PDF

Proc. Amer. Math. Soc. 98 (1986), 119-123 Request permission

Abstract:

We prove that every compact two-dimensional Lorentzian manifold contains a closed timelike or null geodesic. We then construct a two-dimensional example without any closed timelike geodesies and a three-dimensional example without any closed timelike or null geodesics.

References

John K. Beem and Paul E. Ehrlich, Global Lorentzian geometry, Monographs and Textbooks in Pure and Applied Mathematics, vol. 67, Marcel Dekker, Inc., New York, 1981. MR 619853
Gregory J. Galloway, Closed timelike geodesics, Trans. Amer. Math. Soc. 285 (1984), no. 1, 379–388. MR 748844, DOI 10.1090/S0002-9947-1984-0748844-6
Gregory J. Galloway, Splitting theorems for spatially closed space-times, Comm. Math. Phys. 96 (1984), no. 4, 423–429. MR 775039
Robert P. Geroch, Topology in general relativity, J. Mathematical Phys. 8 (1967), 782–786. MR 213139, DOI 10.1063/1.1705276
S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge Monographs on Mathematical Physics, No. 1, Cambridge University Press, London-New York, 1973. MR 0424186
Barrett O’Neill, Semi-Riemannian geometry, Pure and Applied Mathematics, vol. 103, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. With applications to relativity. MR 719023
Roger Penrose, Techniques of differential topology in relativity, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 7, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1972. MR 0469146
Frank J. Tipler, Existence of closed timelike geodesics in Lorentz spaces, Proc. Amer. Math. Soc. 76 (1979), no. 1, 145–147. MR 534406, DOI 10.1090/S0002-9939-1979-0534406-6