Abstract
We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. We obtain a mathematical setting in which one can study causality independently of geometry and differentiable structure, and which also suggests that spacetime emerges from something discrete.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abramsky, S., Jung, A.: Domain theory. In: Maibaum, T.S.E., Abramsky, S., Gabbay, D.M. (eds.) Handbook of Logic in Computer Science, vol. III. Oxford University Press, Oxford (1994)
Chandrasekhar, S.: The maximum mass of ideal white dwarfs. Astrophysical Journal 74, 81–82 (1931)
Gierz, G., Hoffman, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S.: Continuous lattices and domains. Encyclopedia of Mathematics and its Applications, vol. 93. Cambridge University Press, Cambridge (2003)
Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (1973)
Malement, D.: The class of continuous timelike curves determines the topology of spacetime. J. Math. Phys. 18(7), 1399–1404 (1977)
Martin, K.: The measurement process in domain theory. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 116–126. Springer, Heidelberg (2000)
Martin, K., Panangaden, P.: A domain of spacetime intervals in general relativity. Communications in Mathematical Physics 267(3), 563–586 (2006)
Penrose, R.: Gravitational collapse and space-time singularities. Phys. Rev. Lett. 14, 57–59 (1965)
Penrose, R.: Techniques of differential topology in relativity. Society for Industrial and Applied Mathematics (1972)
Scott, D.: Outline of a mathematical theory of computation. Technical Monograph PRG-2, Oxford University Computing Laboratory (1970)
Sorkin, R.: Spacetime and causal sets. In: D’Olivo, J., et al. (eds.) Relativity and Gravitation: Classical and Quantum. World Scientific, Singapore (1991)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Martin, K., Panangaden, P. (2008). Domain Theory and the Causal Structure of Space-Time. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_46
Download citation
DOI: https://doi.org/10.1007/978-3-540-69407-6_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69405-2
Online ISBN: 978-3-540-69407-6
eBook Packages: Computer ScienceComputer Science (R0)