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The Nonlinear Essence of Gravitational Waves

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Abstract

A critical review of gravitational wave theory is made. It is pointed out that the usual linear approach to the gravitational wave theory is neither conceptually consistent nor mathematically justified. Relying upon that analysis it is argued that—analogously to a Yang-Mills propagating field, which must be nonlinear to carry its gauge charge—a gravitational wave must necessarily be nonlinear to transport its own charge—that is, energy-momentum.

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References

  1. Bonazzola, S., Marck, J.A.: Ann. Rev. Nucl. Part. Sci. 44, 655 (1994)

    Article  ADS  Google Scholar 

  2. Cutler, C., Thorne, K.S.: An overview of gravitational-wave source. In: Proceedings of the 16th International Conference on General Relativity and Gravitation, Durban, South Africa (2001) (gr-qc/0204090)

  3. Flanagan, E.E., Hughes, S.A.: New J. Phys. 7, 204 (2005) (gr-qc/0501041)

    Article  ADS  MathSciNet  Google Scholar 

  4. Cooperstock, F.I.: Mod. Phys. Lett. A 14, 1531 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  5. Cooperstock, F.I.: Ann. Phys. (NY) 282, 115 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. Penrose, R.: Proc. R. Soc. Lond. A 381, 53 (1982)

    ADS  MathSciNet  Google Scholar 

  7. Aguirregabiria, J.M., Chamorro, A., Virbhadra, K.S.: Gen. Relativ. Gravit. 28, 1393 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. Virbhadra, K.S.: Phys. Rev. D 60, 104041 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  9. Babak, S.V., Grishchuck, L.P.: Phys. Rev. D 61, 024038 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  10. Chang, C.C., Nester, J.M.: Phys. Rev. Lett. 83, 1897 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. Freeman, New York (1973)

    Google Scholar 

  12. Synge, J.L.: Relativity: The General Theory. North-Holland, Amsterdam (1960)

    MATH  Google Scholar 

  13. Bondi, H.: Proc. R. Soc. Lond. A 427, 249 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  14. Aldrovandi, R., Pereira, J.G.: An Introduction to Geometrical Physics. World Scientific, Singapore (1995)

    MATH  Google Scholar 

  15. Blanchet, L.: Living Rev. Relativ. 5, 3 (2002)

    ADS  Google Scholar 

  16. Schutz, B.F.: A First Course in General Relativity. Cambridge University Press, Cambridge (1985)

    Google Scholar 

  17. Konopleva, N.P., Popov, V.N.: Gauge Fields. Harwood, Chur (1981)

    MATH  Google Scholar 

  18. Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972)

    Google Scholar 

  19. Ciufolini, I., Wheeler, J.A.: Gravitation and Inertia. Princeton University Press, Princeton (1995)

    MATH  Google Scholar 

  20. Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields, 3rd edn. Pergamon Press, New York (1971)

    Google Scholar 

  21. Leclerc, M.: Geodesic deviation equation and gravitational waves. gr-qc/0605033-v1 and v2 (2006)

  22. Itzykson, C., Zuber, J.B.: Quantum Field Theory. McGraw-Hill, New York (1980)

    Google Scholar 

  23. Møller, C.: Ann. Phys. (NY) 4, 347 (1958)

    Article  MATH  ADS  Google Scholar 

  24. Møller, C.: Mat. Fys. Skr. Dan. Vid. Selsk. 1, 10 (1961)

    Google Scholar 

  25. Inönü, E., Wigner, E.P.: Proc. Natl. Acad. Sci. 39, 510 (1953)

    Article  MATH  ADS  Google Scholar 

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Correspondence to J. G. Pereira.

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Aldrovandi, R., Pereira, J.G. & Vu, K.H. The Nonlinear Essence of Gravitational Waves. Found Phys 37, 1503–1517 (2007). https://doi.org/10.1007/s10701-007-9180-2

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  • DOI: https://doi.org/10.1007/s10701-007-9180-2

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