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We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to $C^{1,1}$.
Whitehead, J. H. C. Convex regions in the geometry of paths. Q. J. Math., Oxf. Ser. 3, 33–42, 1932. Addendum, ibid. 4, 226, 1933
1933
Earlier work this paper cites.
Hartman, P, On geodesic coordinates. Am. J. Math., 73 949-954, 1951
1951
Earlier work this paper cites.
Hartman, P., Wintner, A., On the problems of geodesics in the small. Amer. J. Math. 73, 132–148 1951
1951
Earlier work this paper cites.
Lichnerowicz, A.: Théories relativistes de la gravitation et de l’électromgnétisme. Masson, Paris, 1955
1955
Earlier work this paper cites.
Choquet-Bruhat, Y., Geroch, R.: Global aspects of the Cauchy problem in general relativity, Commun. Math. Phys. 14, 329–335, 1969
1969
Earlier work this paper cites.
Penrose, R.: Techniques of Differential Topology in Relativity (Conf. Board of the Mathematical Sciences Regional Conf. Series in Applied Mathematics vol 7) (Philadelphia, PA: SIAM), 1972
1972
Earlier work this paper cites.
Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. Cambridge University Press, 1973
1973
Earlier work this paper cites.
Hirsch, M.W.: Differential topology. Springer, 1976
1976
Earlier work this paper cites.
O’Neill, B.: Semi-Riemannian Geometry. With Applications to Relativity. Pure and Applied Mathematics 103. Academic Press, New York, 1983
1983
Earlier work this paper cites.
Amann, H.: Ordinary Differential Equations. De Gruyter, 1990
1990
Earlier work this paper cites.
Clarke, C. J. S. The analysis of spacetime singularities
1993
Cited alongside, same era.
Beem, J. K., Ehrlich, P. E., Easley, K. L.: Global Lorentzian Geometry (Monographs and Textbooks in Pure and Applied Mathematics vol 202) 2nd edn., New York, Dekker, 1996
1996
Cited alongside, same era.
Sorkin, R. D., Woolgar E., A Causal Order for Spacetimes with C 0 C^{0} Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves Class. Quantum Grav. 13, 1971-1994, 1996
1996
Cited alongside, same era.
Senovilla, J. M. M.: Singularity Theorems and Their Consequences, Gen. Rel. Grav. 30, no 5, 701-848, 1998
1998
Cited alongside, same era.
Kriele, M.: Spacetime. Foundations of general relativity and differential geometry. Lecture Notes in Physics 59, Springer, 1999
1999
Cited alongside, same era.
Maxwell, D.: Rough solutions of the Einstein constraint equations, J. Reine Angew. Math. 590, 1–29, 2006
2006
Later among the works it cites.
Minguzzi, E., Sanchez, M., The causal hierarchy of spacetimes in Recent developments in pseudo-Riemannian geometry
2008
Later among the works it cites.
Chen, B.-L., LeFloch, P., Injectivity Radius of Lorentzian Manifolds, Comm. Math. Phys., 278, 679-713, 2008
2008
Later among the works it cites.
Griffiths, J., Podolský, J.: Exact Space-Times in Einstein’s General Relativity. Cambridge University Press, 2009
2009
Later among the works it cites.
Fathi, A., Siconolfi, A. On smooth time functions. Math. Proc. Camb. Phil. Soc. 155, 1–37, 2011
2011
Later among the works it cites.
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Grosser, M., Kunzinger, M., Oberguggenberger, M., Steinbauer, R.: Geometric theory of generalized functions, Kluwer, 2001
2001
Cited alongside, same era.
Lindenstrauss, J., Preiss, D.: On Fréchet differentiability of Lipschitz maps between Banach spaces, Ann. of Math. 157
2003
Cited alongside, same era.
Klainerman, S., and Rodnianski, I.: Rough solution for the Einstein vacuum equations, Ann. Math. 161(2), 1143-1193, 2005
2005
Cited alongside, same era.
García-Parrado, A., Senovilla, J. M. M.: Causal structures and causal boundaries, Classical Quantum Gravity 22, R1-R84, 2005
2005
Cited alongside, same era.
Chruściel, P.T.: Elements of causality theory, arXiv:1110.6706
Cited in the paper.
Minguzzi, E.: Convex neighborhoods for Lipschitz connections and sprays, arXiv:1308.6675
Cited in the paper.
2012
Later among the works it cites.
Chruściel, P.T., Grant, J.D.E., On Lorentzian causality with continuous metrics, Classical Quantum Gravity 29, no. 14, 145001, 32 pp, 2012
2012
Later among the works it cites.
Hörmann, G., Kunzinger, M., Steinbauer, R.: Wave equations on non-smooth space-times. Evolution equations of hyperbolic and Schrödinger type, 163–186, Progr. Math., 301, Birkhäuser/Springer, 2012
2012
Later among the works it cites.
Kunzinger, M., Steinbauer, R., Stojković, M.: The exponential map of a C 1 , 1 C^{1,1} -metric, Differential Geom. Appl. 34, 14–24, 2014
2014
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