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Signal spaces—an axiomatic approach to space-time

  • Peter Szekeres (a1)
Abstract

An axiomatic approach to relativity theory is proposed which is based entirely on a single reflexive relation called signalling. This generalises and simplifies earlier schemes of Kronheimer and Penrose and of Carter which are based on causality relations. Many of the features of space-times, such as photon paths and topology, have their counterparts in general signal spaces.

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Copyright
References
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[1]Carter, B., ‘Causal structure in space-time’, Gen. Relativity Gravitation 1 (1971), 349391.
[2]Göbel, R., ‘Zeeman topologies on space-times of general relativity theory’, Comm. Math. Phys. 46 (1976), 289307.
[3]Gödel, K., ‘An example of a new type of cosmological solution of Einstein’s field equations of gravitation’, Rev. Modern Phys. 21 (1949), 447450.
[4]Hawking, S.W. and Ellis, G.F.R., The large scale structure of space-time (Cambridge University Press, 1973).
[5]Hawking, S.W., King, A.R. and McCarthy, P.J., ‘A new topology for curved space-time which incoroprates the Causal differential and conformal structures’, J. Math. Phys. 17 (1976), 174181.
[6]Kronheimer, E.H. and Penrose, R., ‘On the structure of Causal spaces’, in Proc. Camb. Phil. Soc. 63, pp. 481501, 1967.
[7]Penrose, R., The Emperor’s new mind, pp. 204 (Oxford University Press, 1989).
[8]Schutz, J.W., Foundations of special relativity: kinematic axioms for Minkowski space-time: Lecture Notes in Mathematics 361 (Springer-Verlag, Berlin, Heidelberg, New York, 1973).
[9]Szekeres, G., ‘Kinematic geometry; and axiomatic system for Minkowski space-time’, J. Austral. Math. Soc. 8 (1968), 134160.
[10]Zeeman, E.C., ‘The topology of Minkowski space’, Topology 6 (1967), 161170.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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