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Some Global Results for Asymptotically Simple Space-Times

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The Conformal Structure of Space-Time

Part of the book series: Lecture Notes in Physics ((LNP,volume 604))

Abstract

A uniqueness theorem for Minkowski space and de Sitter space associated with the occurrence of null lines (inextendible globally achronal null geodesics) is presented. This result is obtained as a consequence of the null splitting theorem, which is also discussed.

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References

  1. L. Andersson and G. J. Galloway, dS/CFT and spacetime topology, preprint, hepth/0202161.

    Google Scholar 

  2. L. Andersson, G. J. Galloway, and R. Howard, A strong maximum principle for weak solutions of quasi-linear elliptic equations with applications to Lorentzian and Riemannian geometry, Comm. Pure Appl. Math. 51, 581–624 (1998).

    Article  MathSciNet  Google Scholar 

  3. P. T. Chruściel, E. Delay, G. J. Galloway, and R. Howard, Regularity of horizons and the area theorem, Ann. Henri Poincaré 2, 109–178 (2001).

    Article  MATH  ADS  Google Scholar 

  4. J. L. Friedman, K. Schleich, and D. M. Witt, Topological censorship, Phys. Rev. Lett. 71, 1486–1489 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  5. H. Friedrich, On the existence of n-geodesically complete or future complete solutions of Einstein’s field equations with smooth asymptotic structure., Comm. Math. Phys. 107, 587–609 (1986).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. H. Friedrich, Existence and structure of past asymptotically simple solutions of Einstein’s field equations with positive cosmological constant, J. Geom. Phys. 3, 101–117 (1986).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. H. Friedrich, On the global existence and the asymptotic behaviour of solutions to the Einstein-Maxwell-Yang-Mills equations, J. Diff. Geom. 3, 275–345 (1991).

    MathSciNet  Google Scholar 

  8. H. Friedrich, Einstein’s equation and conformal structure, in The Geometric universe: Science, geometry and the work of Roger Penrose, eds. S. A. Huggett et al., Oxford University Press, Oxford, 1996.

    Google Scholar 

  9. H. Friedrich, Einstein’s equations and geometric asymptotics, in Gravitation and relativity: At the turn of the millennium. Proceedings of the GR-15 Conference at Pune, India, in June 1997, eds. N. Dadhich and J. Narlikar, IUCAA, Pune, India.

    Google Scholar 

  10. G. J. Galloway, Maximum Principles for null hypersurfaces and null splitting theorems, Ann. Henri Poincaré 1, 543–567 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  11. G. Galloway, K. Schleich, D. Witt, and E. Woolgar, Topological Censorship and Higher Genus Black Holes, Phys. Rev. D 60, 104039 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  12. G. J. Galloway, S. Surya and E. Woolgar, A uniqueness theorem for the AdS soliton, Phys. Rev. Lett. 88, 101102 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  13. S. Gao and R. M. Wald, Theorems on gravitational time delay and related issues, Class. Quant. Grav. 17, 4999–5008 (2000).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press, Cambridge, 1973.

    Book  MATH  Google Scholar 

  15. L. J. Mason, The asymptotic structure of algebraically special spacetimes, Class. Quantum Grav. 15, 1019–1030 (1998).

    Article  MATH  ADS  Google Scholar 

  16. R.P.A.C. Newman, The global structure of simple space-times, Commun. Math. Phys. 123, 17–52 (1989).

    Article  MATH  ADS  Google Scholar 

  17. B. O’Neill, Semi-Riemannian geometry, Academic Press, New York, 1983.

    Google Scholar 

  18. R. Penrose, Zero rest-mass fields including gravitation: asymptotic behavior, Proc. Roy. Soc. Lond. A 284, 159–203 (1965).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. R. Penrose, Techniques of differential topology in relativity, SIAM, Philadelphia, 1972, (Regional Conf. Series in Appl. Math., vol. 7).

    MATH  Google Scholar 

  20. R. Penrose and W. Rindler, Spinors and Spacetime, vol. 2, chapter 9, Cambridge University Press, Cambridge, 1986.

    Book  Google Scholar 

  21. R. Penrose, R. D. Sorkin and E. Woolgar, A positive mass theorem based on the focusing and retardation of null geodesics, preprint, gr-qc/9301015.

    Google Scholar 

  22. R. M. Wald, General relativity, University of Chicago Press, Chicago, 1984.

    MATH  Google Scholar 

  23. E. Woolgar, The positivity of energy for asymptotically anti-de Sitter spacetimes, Class. Quant. Grav. 11, 1881–1900 (1994).

    Article  MATH  ADS  MathSciNet  Google Scholar 

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Galloway, G.J. (2002). Some Global Results for Asymptotically Simple Space-Times. In: Frauendiener, J., Friedrich, H. (eds) The Conformal Structure of Space-Time. Lecture Notes in Physics, vol 604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45818-2_2

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  • DOI: https://doi.org/10.1007/3-540-45818-2_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44280-6

  • Online ISBN: 978-3-540-45818-0

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