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Almost Birkhoff theorem in general relativity

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Abstract

We extend Birkhoff’s theorem for almost LRS-II vacuum spacetimes to show that the rigidity of spherical vacuum solutions of Einstein’s field equations continues even in the perturbed scenario.

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References

  1. Birkhoff G.D.: Relativity and Modern Physics. Harvard University Press, Cambridge, MA (1923)

    MATH  Google Scholar 

  2. Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Spacetime. Cambridge University Press, Cambridge (1973) Appendix B

  3. Stoeger W., Maartens R., Ellis G.F.R.: Proving almost-homogeneity of the universe: an almost-Ehlers, Geren and Sachs theorem. Ap. J. 443, 1–5 (1995)

    Article  ADS  Google Scholar 

  4. Ehlers J., Geren P., Sachs R.K.: Isotropic solutions of Einstein-Liouville equations. J. Math. Phys. 9, 1344 (1968)

    Article  ADS  Google Scholar 

  5. Bondi H.: Spherically symmetric models in general relativity. Mon. Not. Roy. Astr. Soc. 107, 410 (1947)

    MathSciNet  ADS  MATH  Google Scholar 

  6. D’Inverno, R.: Introducing Einstein’s Relativity. Clarendon Press, Oxford (1992) Section 18.1

  7. Faraoni, V.: Cosmology in Scalar-Tensor Gravity. Fundamental Theories of Physics, Springer, Berlin (2004)

  8. Clarkson C.A., Barrett R.K.: Class. Quantum Gravity 20, 3855 (2003) [gr-qc/0209051]

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Clarkson C.: Phys. Rev. D 76, 104034 (2007) [arXiv:0708.1398(gr-qc)]

    Article  MathSciNet  ADS  Google Scholar 

  10. Ehlers, J.: Abh. Mainz Akad. Wiss. u. Litt. (Math. Nat. kl) 11, (1961)

  11. Ellis, G.F.R.: General relativity and cosmology. In: Sachs, R.K. (ed.) Proceedings of XLVII Enrico Fermi Summer School, New York Academic Press, New York (1971)

  12. Ellis, G.F.R., van Elst, H.: Cosmological models (Cargèse lectures 1998). In: Lachièze-Rey, M. (ed.) Theoretical and Observational Cosmology, p. 1. Kluwer, Dordrecht (1999)

  13. Ellis G.F.R.: The dynamics of pressure-free matter in general relativity. J. Math. Phys. 8, 1171–1194 (1967)

    Article  ADS  Google Scholar 

  14. van Elst H., Ellis G.F.R.: Class. Quantum Gravity 13, 1099 (1996) [gr-qc/9510044]

    Article  ADS  MATH  Google Scholar 

  15. Betschart G., Clarkson C.A.: Class. Quantum Gravity 21, 5587 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  16. Frolov V.P., Shoom A.A.: Phys. Rev. D 76, 064037 (2007) [arXiv:0705.1570 (gr-qc)]

    Article  MathSciNet  ADS  Google Scholar 

  17. Vishveshwara C.V.: Stability of the Schwarzschild metric. Phys. Rev. D 1, 2870–2879 (1970)

    Article  ADS  Google Scholar 

  18. Chandrasekhar S.: On the equations governing the perturbations of the Schwarzschild black hole. Proc. R. Soc. Lond. A 343, 289 (1975)

    Article  MathSciNet  ADS  Google Scholar 

  19. Ellis G.F.R., Uzan J.-P., Larena J.: A two-mass expanding exact space time solution. Gen. Relativ. Gravit. 43, 191–205 (2010) [arXiv:1005.1809]

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. ACGC and Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701, South Africa

    Rituparno Goswami & George F. R. Ellis

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  1. Rituparno Goswami
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  2. George F. R. Ellis
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Correspondence to Rituparno Goswami.

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Goswami, R., Ellis, G.F.R. Almost Birkhoff theorem in general relativity. Gen Relativ Gravit 43, 2157–2170 (2011). https://doi.org/10.1007/s10714-011-1172-z

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  • DOI: https://doi.org/10.1007/s10714-011-1172-z

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