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Domain Theory and General Relativity

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New Structures for Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 813))

Abstract

We discuss the current state of investigations into the domain theoretic structure of spacetime, including recent developments which explain the connection between measurement, the Newtonian concept of time and the Lorentz distance.

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Notes

  1. 1.

    The results in the present paper work for any dimension \(n\geq 2\) [J93].

  2. 2.

    This terminology is common among relativists but order theorists use the phrase “Alexandrov topology” to mean something else: the topology generated by the upper sets.

References

  1. 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)

    Google Scholar 

  2. Beem, J.K., Ehrlich, P.E., Easley, K.L.: Global Lorentzian Geometry. CRC Press, Boca Raton (1996)

    MATH  Google Scholar 

  3. Chandrasekhar, S.: The maximum mass of ideal white dwarfs. Astrophys. J. 74, 81–82 (1931)

    Article  ADS  MATH  Google Scholar 

  4. Fajstrup, L.: Loops, ditopology and deadlocks: Geometry and concurrency. Math. Struct. Comput. Sci. 10(4), 459–480 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Goubault, E., Fajstrup, L., Raussen, M.: Algebraic topology and concurrency. Department of Mathematical Sciences RR-98–2008, Aalborg University, 1998. Presented at MFCS 1998 London

    Google Scholar 

  6. Gierz, G., Hoffman, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S.: Continuous lattices and domains. Number 93 in Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  7. Hawking, S.W., Ellis, G.F.R. The large scale structure of space-time. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (1973)

    Book  Google Scholar 

  8. Joshi, P.S.: Global aspects in gravitation and cosmology. International Series of Monographs on Physics 87. Oxford Science Publications, Oxford (1993)

    Google Scholar 

  9. Malement, D.: The class of continuous timelike curves determines the topology of spacetime. J. Math. Phys. 18(7), 1399–1404 (1977)

    Article  ADS  Google Scholar 

  10. Martin, K.: A foundation for computation. PhD thesis, Department of Mathematics, Tulane University (2000)

    Google Scholar 

  11. Martin K.: The measurement process in domain theory. In: Proceedings of the 27th International Colloquium on Automata, Languages and Programming (ICALP’00), Number 1853 in Lecture Notes In Computer Science, pp. 116–126. Springer, New York (2000)

    Google Scholar 

  12. Martin, K. Compactness of the space of causal curves. J. Class. Quant. Grav. 23, 1241–1251 (2006)

    Article  ADS  MATH  Google Scholar 

  13. Martin, K., Panangaden, P.: A domain of spacetime intervals in general relativity. Commun. Math. Phys. 267(3), 563–586 (November 2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Penrose, R.: Gravitational collapse and space-time singularities. Phys. Rev. Lett. 14, 57–59 (1965)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Penrose, R.: Techniques of differential topology in relativity. Society for Industrial and Applied Mathematics (1972)

    Google Scholar 

  16. Penrose, R., Sorkin, R.D., Woolgar, E.: A positive mass theorem based on the focusing and retardation of null geodesics. Submitted to Commun. Math. Phys., arXiv:grqc/9301015 (1993)

    Google Scholar 

  17. Scott, D.: Outline of a mathematical theory of computation. Technical Monograph PRG-2, Oxford University Computing Laboratory (1970)

    Google Scholar 

  18. Sorkin, R.: Spacetime and causal sets. In: D’Olivo J. et. al. (eds.) Relativity and Gravitation: Classical and Quantum. World Scientific, Singapore (1991)

    Google Scholar 

  19. Sorkin, R.D., Woolgar, E.: A causal order for spacetimes with c 0 Lorentzian metrics: Proof of compactness of the space of causal curves. Class. Quant. Grav. 13, 1971–1994 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Wald, R.M.: General Relativity. The University of Chicago Press, Chicago (1984)

    Book  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Naval Research Laboratory, Washington, DC, USA

    P. Panangaden

Authors
  1. K. Martin
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  2. P. Panangaden
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Corresponding authors

Correspondence to K. Martin or P. Panangaden .

Editor information

Editors and Affiliations

  1. Parks Road, Oxford, OX1 3QD, United Kingdom

    Bob Coecke

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Martin, K., Panangaden, P. (2010). Domain Theory and General Relativity. In: Coecke, B. (eds) New Structures for Physics. Lecture Notes in Physics, vol 813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12821-9_11

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  • DOI: https://doi.org/10.1007/978-3-642-12821-9_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12820-2

  • Online ISBN: 978-3-642-12821-9

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