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Year 2014, Volume: 11 Issue: 2, - , 01.11.2014

Abstract

References

  • [1] S. Abramsky, A. Jung, Domain theory, Handbook of Logic in Computer Science, S. Abramsky, D. M. Gabbay, T. S. E. Maibaum (Editors), Volume III, Oxford University Press (1994).
  • [2] J. K. Beem, P. E. Ehrlich, K. L. Easley, Global Lorentzian Geometry, Marcel Dekker, New York, (1996).
  • [3] B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, 2nd Edition, Cambridge University Press, (2002).
  • [4] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lowson, M. Mislove, D. S. Scott, Continuous Lattices and Domains, Encyclopedia Math. Appl. 93, Cambridge University Press, (2003).
  • [5] S. W. Hawking and G. F. R. Ellis, The large scale structure of spacetime, Cambridge Monographs on Mathematical Physics, Cambridge University Press, (1972).
  • [6] K. Keimel, Bicontinuous Domains and some old problems in Domain theory, Electron. Notes Theor. Comput. Sci., 257, (2009), 35–54.
  • [7] K. Martin, P. Panangaden, Spacetime topology from causality, Arxiv gr-qc/0407093v1, (2004).
  • [8] K. Martin, P. Panangaden, ‘A domain of spacetime intervals in General Relativity”, Commun. Math. Phys. 267, (2006), 563–586.
  • [9] R. Penrose, Techniques of differential topology in Relativity, AMS Colloquium Publications, SIAM Philadelphia, (1972).
  • [10] D. Scott, Outline of a mathematical theory of computation, Technical Monograph PRG-2, Oxford University Computing Laboratory, (1970).
  • [11] Alex Simoson, Part III: Topological Spaces from a Computational Perspective, Mathematical Structures for Semantics, (2001-2002).
  • [12] R. M. Wald, General Relativity, University of Chicago Press, (1984).

Causally Simple Spacetimes and Domain Theory

Year 2014, Volume: 11 Issue: 2, - , 01.11.2014

Abstract

Globally, hyperbolic spacetimes are the simplest kind of spacetimes which are studied in General
Relativity. It is shown by Martin and Panangaden that it is possible to reconstruct globally hyperbolic spacetimes
in a purely order theoretic manner using the causal relation J
+. Indeed these spacetimes belong to a
category that is equivalent to a special category of domains known as interval domains [8]. In this paper, it is
shown that this result is true for a larger superclass of spacetimes.

References

  • [1] S. Abramsky, A. Jung, Domain theory, Handbook of Logic in Computer Science, S. Abramsky, D. M. Gabbay, T. S. E. Maibaum (Editors), Volume III, Oxford University Press (1994).
  • [2] J. K. Beem, P. E. Ehrlich, K. L. Easley, Global Lorentzian Geometry, Marcel Dekker, New York, (1996).
  • [3] B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, 2nd Edition, Cambridge University Press, (2002).
  • [4] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lowson, M. Mislove, D. S. Scott, Continuous Lattices and Domains, Encyclopedia Math. Appl. 93, Cambridge University Press, (2003).
  • [5] S. W. Hawking and G. F. R. Ellis, The large scale structure of spacetime, Cambridge Monographs on Mathematical Physics, Cambridge University Press, (1972).
  • [6] K. Keimel, Bicontinuous Domains and some old problems in Domain theory, Electron. Notes Theor. Comput. Sci., 257, (2009), 35–54.
  • [7] K. Martin, P. Panangaden, Spacetime topology from causality, Arxiv gr-qc/0407093v1, (2004).
  • [8] K. Martin, P. Panangaden, ‘A domain of spacetime intervals in General Relativity”, Commun. Math. Phys. 267, (2006), 563–586.
  • [9] R. Penrose, Techniques of differential topology in Relativity, AMS Colloquium Publications, SIAM Philadelphia, (1972).
  • [10] D. Scott, Outline of a mathematical theory of computation, Technical Monograph PRG-2, Oxford University Computing Laboratory, (1970).
  • [11] Alex Simoson, Part III: Topological Spaces from a Computational Perspective, Mathematical Structures for Semantics, (2001-2002).
  • [12] R. M. Wald, General Relativity, University of Chicago Press, (1984).
There are 12 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Neda Ebrahimi This is me

Publication Date November 1, 2014
Published in Issue Year 2014 Volume: 11 Issue: 2

Cite

APA Ebrahimi, N. (2014). Causally Simple Spacetimes and Domain Theory. Cankaya University Journal of Science and Engineering, 11(2).
AMA Ebrahimi N. Causally Simple Spacetimes and Domain Theory. CUJSE. November 2014;11(2).
Chicago Ebrahimi, Neda. “Causally Simple Spacetimes and Domain Theory”. Cankaya University Journal of Science and Engineering 11, no. 2 (November 2014).
EndNote Ebrahimi N (November 1, 2014) Causally Simple Spacetimes and Domain Theory. Cankaya University Journal of Science and Engineering 11 2
IEEE N. Ebrahimi, “Causally Simple Spacetimes and Domain Theory”, CUJSE, vol. 11, no. 2, 2014.
ISNAD Ebrahimi, Neda. “Causally Simple Spacetimes and Domain Theory”. Cankaya University Journal of Science and Engineering 11/2 (November 2014).
JAMA Ebrahimi N. Causally Simple Spacetimes and Domain Theory. CUJSE. 2014;11.
MLA Ebrahimi, Neda. “Causally Simple Spacetimes and Domain Theory”. Cankaya University Journal of Science and Engineering, vol. 11, no. 2, 2014.
Vancouver Ebrahimi N. Causally Simple Spacetimes and Domain Theory. CUJSE. 2014;11(2).