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Prog. Theor. Phys. Vol. 110 No. 4 (2003) pp. 723-755

[ Full Text PDF : FREE ACCESS (299K) ]

Gauge Invariant Variables in Two-Parameter Nonlinear Perturbations

Kouji Nakamura*

Division of Theoretical Astrophysics, National Astronomical Observatory, Mitaka 181-8588, Japan

(Received March 24, 2003)

Abstract:

The procedure to find gauge invariant variables for two-parameter nonlinear perturbations in general relativity is considered. For each order metric perturbation, we define the variable which is defined by the appropriate combination with lower order metric perturbations. Under the gauge transformation, this variable is transformed in the manner similar to the gauge transformation of linear order metric perturbation. We confirm this up to third order. This implies that gauge invariant variables for higher order metric perturbations can be found by using a procedure similar to that for linear order metric perturbations. We also derive gauge invariant combinations for the perturbation of an arbitrary physical variable, other than the spacetime metric, up to third order.


URL : http://ptp.ipap.jp/link?PTP/110/723/
DOI : 10.1143/PTP.110.723


*E-mail: kouchan@th.nao.ac.jp

[ Full Text PDF : FREE ACCESS (299K) ] Citation:

References:

  1. D. Kramer, H. Stephani, M. A. H. MacCallum and E. Herlt, Exact Solutions of Einstein's Field Equations (Cambridge: Cambridge University Press, 1980).
  2. J. M. Bardeen, Phys. Rev. D 22 (1980), 1882[APS].
  3. H. Kodama and M. Sasaki, Prog. Theor. Phys. Suppl. No. 78 (1984), 1[PTP].
  4. V. F. Mukhanov, H. A. Feildman and R. H. Brandenberger, Phys. Rep. 215 (1992), 203[CrossRef].
  5. S. Chandrasekhar, The mathematical theory of black holes (Oxford: Clarendon Press, 1983).
  6. R. J. Gleiser, C. O. Nicasio, R. H. Price and J. Pullin, Phys. Rep. 325 (2000), 41[CrossRef].
  7. K. D. Kokkotas and B. G. Schmidt, Living Rev. Relativity 2 (1999), 2.
  8. Y. Kojima, Prog. Theor. Phys. Suppl. No. 128 (1997), 251[PTP].
  9. J. B. Hartile, Astrophys. J. 150 (1967), 1005[CrossRef].
    S. Chandrasekhar and J. C. Miller, Mon. Not. R. Astron. Soc. 167 (1974), 63.
  10. N. Stergioulas, Living Rev. Relativity 2 (1999), 2.
  11. R. M. Wald, General Relativity (Chicago, IL: University of Chicago Press, 1984).
  12. J. M. Stewart and M. Walker, Proc. R. Soc. London A 341 (1974), 49.
    J. M. Stewart, Class. Quantum Grav. 7 (1990), 1169[CrossRef]; Advanced General Relativity (Cambridge University Press, Cambridge, 1991).
  13. K. Nakamura, Prog. Theor. Phys. 110 (2003), 201[PTP].
  14. M. Bruni, L. Gualtieri and C. F. Sopuerta, Class. Quantum Grav. 20 (2003), 535[CrossRef].
  15. M. Bruni, S. Matarrese, S. Mollerach and S. Sqonego, Class. Quantum Grav. 14 (1997), 2585[CrossRef].
  16. Y. Choquet-Bruhat, C. DeWitt-Morette and M. Dillard-Bleick, Analysis, Manifolds and Physics (North-Holland, Amsterdam, 1982).
  17. S. Sonego and M. Bruni, Commun. Math. Phys. 193 (1998), 209[CrossRef].
  18. W. Thirring, A Course in Mathematical Physics: I. Classical Dynamical Systems (New York, Springer, 1978).
  19. S. Kobayashi and K. Nomizu, Foundation of Differential Geometry vol. I (Wiley, New York, 1963).
  20. S. Matarrese, S. Mollerach and M. Bruni, Phys. Rev. D 58 (1998), 043504[APS].
  21. M. Bruni and S. Sonego, Class. Quantum Grav. 16 (1999), L29[CrossRef].
  22. U. H. Gerlach and U. K. Sengupta, Phys. Rev. D 19 (1979), 2268[APS]; Phys. Rev. D 20 (1979), 3009[APS]; Phys. Rev. D 22 (1980), 1300[APS]; J. Math. Phys. 20 (1979), 2540[CrossRef].
  23. M. Campanelli and C. O. Lousto, Phys. Rev. D 59 (1999), 124022[APS].
  24. K. Nakamura, A. Ishibashi and H. Ishihara, Phys. Rev. D 62 (2000), 101502[APS](R).
    K. Nakamura and H. Ishihara, Phys. Rev. D 63 (2001), 127501[APS].
  25. L. Randall and R. Sundrum, Phys. Rev. Lett. 83 (1999), 4690[APS]; Phys. Rev. Lett. 83 (1999), 3370[APS].
    J. Garriga and T. Tanaka, Phys. Rev. Lett. 84 (2000), 2778[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 113 No. 3 (2005) pp. 481-511 :
    Second-Order Gauge Invariant Perturbation Theory
    Kouji Nakamura
  2. Progress of Theoretical Physics Vol. 117 No. 1 (2007) pp. 17-74 :
    Second-Order Gauge Invariant Cosmological Perturbation Theory
    Kouji Nakamura
  3. Progress of Theoretical Physics Vol. 121 No. 6 (2009) pp. 1321-1360 :
    Consistency of Equations in the Second-Order Gauge-Invariant Cosmological Perturbation Theory
    Kouji Nakamura

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