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Space-time edge geometry

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References

  1. Beem, J. K. (1976). “Conformal changes and geodesic completeness,”Commun. Math. Phys.,49, 179–186.

    Google Scholar 

  2. Beem, J. K. (1976). “Globally hyperbolic space-times which are timelike Cauchy complete,”Gen. Rel. Grav.,7, 339–344.

    Google Scholar 

  3. Beem, J. K. (1976). “Some examples of incomplete space-times,”Gen. Rel. Grav.,7, 501–509.

    Google Scholar 

  4. Bishop, R. L., and Crittenden, R. J. (1964).Geometry of Manifolds (Academic Press, New York).

    Google Scholar 

  5. Bishop, R. L., and Goldberg, S. I. (1968).Tensor Analysis on Manifolds (MacMillan, New York).

    Google Scholar 

  6. Borzeszkowski, H. H. V., and Kasper, U. (1975). “Boundaries of space-times and singularities in general relativity,”Ann. Phys. Leipzig,32, 146–158.

    Google Scholar 

  7. Bosshard, B. (1976). “On theb-boundary of the closed Friedmann model,”Commun. Math. Phys.,46, 263–268.

    Google Scholar 

  8. Brickell, F., and Clark, R. S. (1970).Differentiable Manifolds (Van Nostrand, London).

    Google Scholar 

  9. Campbell, S. J., and Wainwright, J. (1977). “Algebraic computing and the Newman-Penrose formalism in general relativity,” Preprint (Dept. Applied Math., University of Waterloo, Ontario, Canada).

    Google Scholar 

  10. Clarke, C. J. S. (1975). “Singularities in globally hyperbolic space-times,”Commun. Math. Phys.,41, 65–78.

    Google Scholar 

  11. Clarke, C. J. S. (1976). “Space-time singularities,”Commun. Math. Phys.,49, 17–23.

    Google Scholar 

  12. Clarke, C. J. S. (1976). “On the differentiability of space-time,” Preprint MPI-PAE/Astro 80 (Max Planck Institute for Physics and Astrophysics, Munich).

    Google Scholar 

  13. Clarke, C. J. S., and Schmidt, B. G. (1977). “Singularities: The state of the art,”Gen. Rel. Grav.,8, 129–137.

    Google Scholar 

  14. Dieudonné, J. (1960).Foundations of Modern Analysis (Academic Press, New York).

    Google Scholar 

  15. Dodson, C. T. J. “A new bundle-completion for parallelizable spacetimes,” Internal Report IC/77/60 (ICTP, Trieste); presented at GR8 Symposium, Waterloo, Ontario, Canada, August 1977.

  16. Dodson, C. T. J., and Poston, T. (1977).Tensor Geometry (Pitman, London).

    Google Scholar 

  17. Dodson, C. T. J., and Sulley, L. J. (1977). “Theb-boundary ofS 1 with a constant connection,”Lett. Math. Phys.,1, 301–307.

    Google Scholar 

  18. Duncan, D. P., and Shepley, L. C. (1974). “A numerical sufficient condition for deciding if a space-time is inextensible,”Nuovo Cimenta,24B, 130–134.

    Google Scholar 

  19. Duncan, D. P., and Shepley, L. C. (1975). “Boundaries of spacetimes,”J. Math. Phys.,16, 485–492.

    Google Scholar 

  20. Eardley, D., and Sachs, R. K. (1973). “Space-times with a future projective infinity,”J. Math. Phys.,14, 209–212.

    Google Scholar 

  21. Eells, J. (1974). “Fibre bundles,” inGlobal Analysis and Its Applications, vol. I (IAEA, Vienna), pp. 53–82.

    Google Scholar 

  22. Ehresmann, C. (1951). “Les connexions infinitésimales dans un espace fibre différentiable,” Colloque de Topologie, Bruxelles, 5–8 June 1950, CBRM (Georges Thone, Liege), pp. 29–55.

    Google Scholar 

  23. Ellis, G. F. R., and King, A. R. (1974). “Was the big-bang a whimper?”Commun, Math. Phys.,38, 119–156.

    Google Scholar 

  24. Ellis, G. F. R., and Schmidt, B. G. (1976). “Singular space-times”, Preprint MPI-PAE/Astro 104 (Max Planck Institute for Physics and Astrophysics, Munich).

    Google Scholar 

  25. Friedrich, H. (1974). “Construction and properties of space-timeb-boundaries,”Gen. Rel. Grav.,5, 681–697.

    Google Scholar 

  26. Geroch, R. P. (1967). “Topology in general relativity,”J. Math. Phys.,8, 782–786.

    Google Scholar 

  27. Geroch, R. P. (1968). “Spinor structures of spacetimes in general relativity. I,”J. Math. Phys.,9, 1739–1744.

    Google Scholar 

  28. Geroch, R. “Local characterization of singularities in general relativity,”J. Math. Phys.,9, 450–465.

  29. Geroch, R. P. (1968). “What is a singularity?”Ann. Phys.,48, 526–540.

    Google Scholar 

  30. Geroch, R., Kronheimer, E. H., and Penrose, R. (1972). “Ideal points in spacetime,”Proc. R. Soc. Lond. A.,327, 545–567.

    Google Scholar 

  31. GR8Abstracts of Contributed Papers, Eighth International Conference on General Relativity and Gravitation, August 7–12, 1977, Department of Applied Mathematics, University of Waterloo, Ontario, Canada.

  32. Hájiček, P., and Schmidt, B. G. (1971). “Theb-boundary of tensor bundles over a space-time,”Commun. Math. Phys.,23, 285–295.

    Google Scholar 

  33. Hawking, S. W. (1966). “Singularities and the geometry of space-time,” Adams Prize Essay, Cambridge (unpublished).

    Google Scholar 

  34. Hawking, S. W. (1971). InProceedings of Liverpool Singularities Symposium II, Lecture Notes in Mathematics 209 (Springer, Berlin), pp. 275–279.

    Google Scholar 

  35. Hawking, S. W., and Ellis, G. F. R. (1973).The Large-Scale Structure of Spacetime (Cambridge University Press, Cambridge).

    Google Scholar 

  36. Hurewicz, W., and Wallman, H. (1948).Dimension theory (Princeton University Press, Princeton).

    Google Scholar 

  37. Ihrig, E. (1976). “The holonomy group in general relativity and the determination ofg if fromT ij ”,Gen. Rel. Grav.,7, 313–323.

    Google Scholar 

  38. Johnson, R. A. (1977). “The bundle boundary in some special cases,”J. Math. Phys.,18, 898–902.

    Google Scholar 

  39. Kelley, J. L. (1965).General Topology (van Nostrand, Princeton).

    Google Scholar 

  40. King, A. R., and Ellis, G. F. R. (1973). “Tilted homogeneous cosmological models,”Commun. Math. Phys.,31, 209–242.

    Google Scholar 

  41. Kobayashi, S., and Nomizu, K. (1963).Foundations of Differential Geometry, vol. 1 (Interscience, New York).

    Google Scholar 

  42. Kowalsky, H-J. (1965).Topological spaces (Academic Press, New York).

    Google Scholar 

  43. Kronheimer, E. H., and Penrose, R. (1967). “On the structure of causal spaces,”Proc. Camb. Phil. Soc.,63, 481–501.

    Google Scholar 

  44. Lee, C. W. (1977). “A restriction on the topology of Cauchy surfaces in general relativity,”Commun. Math. Phys.,51, 157–162.

    Google Scholar 

  45. Lee, C. W. (1977). “Implicit restrictions on the topology of space-time,” Ph.D. thesis, Dept. Mathematics, University of Lancaster [see also Proc. Roy. Soc. 1978].

  46. Lee, K. K. (1973). “Global spinor fields in space-time,”Gen. Rel. Grav.,4, 421–433.

    Google Scholar 

  47. Lee, K. K. (1975). “On the fundamental groups of space-times in general relativity,”Gen. Rel. Grav.,6, 239–242.

    Google Scholar 

  48. Marathe, K. B. (1972). “A condition for paracompactness of a manifold,”J. Diff. Geom.,7, 571–573.

    Google Scholar 

  49. Parker, P. E. (1977). “The Schwarzschild particle,” Preprint (Dept. Mathematics, State University of New York at Buffalo).

    Google Scholar 

  50. Penrose, R. (1969). “Structure of space-time,” inBattelle Rencontres, ed. C. M. De Witt and J. A. Wheeler (Benjamin, New York), pp. 121–235.

    Google Scholar 

  51. Pontryagin, L. S. (1966).Topological Groups, 2nd ed. (Gordon and Breach, New York).

    Google Scholar 

  52. Sachs, R. K. (1973). “Spacetimeb-boundaries,”Commun. Math. Phys.,33, 215–220.

    Google Scholar 

  53. Sachs, R. K., and Wu, H. (1976).General Relativity for Mathematicians (Springer-Verlag, New York and Berlin).

    Google Scholar 

  54. Schmidt, B. G. (1968). “Riemannsche Räume mit mehrfach transitiver Isometrie-gruppe,” Doktorarbeit, University of Hamburg.

  55. Schmidt, B. G. (1971). “A new definition of singular points in general relativity,”Gen. Rel. Grav.,1, 269–280.

    Google Scholar 

  56. Schmidt, B. G. (1973). “Local completeness of theb-boundary,”Commun. Math. Phys.,29, 49–54.

    Google Scholar 

  57. Schmidt, B. G. (1974). “A new definition of conformal and projective infinity of spacetimes,”Commun. Math. Phys.,36, 73–90.

    Google Scholar 

  58. Seifert, H-J. (1971). “The causal boundary of space-times,”Gen. Rel. Grav.,1, 247–259.

    Google Scholar 

  59. Stredder, P. (1975). “Natural differential operators on Riemannian manifolds and representations of the orthogonal and special orthogonal groups,”J. Diff. Geom.,10, 647–660.

    Google Scholar 

  60. Steenrod, N. E. (1951).Topology of Fibre Bundles (Princeton University Press, Princeton).

    Google Scholar 

  61. Thorpe, J. E. (1969). “Curvature and the Petrov canonical forms,”J. Math. Phys.,10, 1–7.

    Google Scholar 

  62. Thorpe, J. E. (1977). “Curvature invariants and space-time singularities,”J. Math. Phys.,18, 960–964.

    Google Scholar 

  63. Tipler, F. J. (1977). “On the nature of singularities in general relativity,”Phys. Rev. D.,15, 942–945.

    Google Scholar 

  64. Woodhouse, N. M. J. (1974). “The completion of a chronological space,”Proc. Camb. Phil. Soc.,76, 531–544.

    Google Scholar 

  65. Woodhouse, N. M. J. (1976). “An application of Morse theory to space-time geometry,”Commun. Math. Phys.,46, 135–152.

    Google Scholar 

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  1. Department of Mathematics, University of Lancaster, UK

    C. T. J. Dodson

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Dodson, C.T.J. Space-time edge geometry. Int J Theor Phys 17, 389–504 (1978). https://doi.org/10.1007/BF00670382

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