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Stability of the intrinsic energy vanishing in the Schwarzschild metric under a slow rotation

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Abstract

The linearized Kerr metric is considered and put in some Gauss coordinates which are further intrinsic ones. The linear and angular 4-momenta of this metric are calculated in these coordinates and the resulting value is just zero. Thus, the global vanishing previously found for the Schwarzschild metric remains linearly stable under slow rotational perturbations of this metric.

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References

  1. Gourgoulhon, É.: 3+1 Formalism and bases of Numerical Relativity, Lecture Notes in Physics 846, Springer (2012)

  2. Alcubierre, M.: Introduction to \(3+1\) Numerical Relativity. Oxford University Press, (2008)

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

    Article  ADS  MATH  MathSciNet  Google Scholar 

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

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. Cooperstock, F.I., Dupre, M.J.: Ann. Phys. Amsterdam 339, 531 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  6. Lemaître, G.: Ann. Soc. Sci. Bruxeles A 53, 51 (1933) Golden Oldie Republication. Gen. Relativ. Gravit. 29, 641 (1997)

  7. Zannias, T.: Phys. Rev. D 49, 6928 (1994)

    Article  ADS  Google Scholar 

  8. Chruściel, P.T.: Class. Quantum Gravity 3, L115 (1986)

    Article  MATH  Google Scholar 

  9. Lapiedra, R., Morales-Lladosa, J.A.: Gen. Relativ. Gravit. 45, 1145 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  10. Ferrando, J.J., Lapiedra, R., Morales, J.A.: Phys. Rev. D 75, 124003 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  11. Lapiedra, R., Sáez, D.: Phys. Rev. D 77, 104011 (2008)

    Article  ADS  Google Scholar 

  12. Lapiedra, R., Morales-Lladosa, J.A.: Gen. Relativ. Gravit. 44, 367 (2012)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  13. Albrow, M.G.: Nature 241, 56 (1973)

    ADS  Google Scholar 

  14. Tryon, E.P.: Nature 246, 396 (1973)

    Article  ADS  Google Scholar 

  15. Vilenkin, A.: Phys. Rev. D 32, 2511 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  16. Lapiedra, R., Morales-Lladosa, J.A.: Phys. Rev. D 89, 064033 (2014)

    Article  ADS  Google Scholar 

  17. Mashhoon, B., Hehl, F.W., Theiss, D.S.: Gen. Relativ. Gravit. 16, 711 (1984)

    Article  ADS  MathSciNet  Google Scholar 

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

  19. Oppenheimer, J.R., Snyder, H.: Phys. Rev. 56, 455 (1939)

  20. Synge, J.L.: Proc. Roy. Irish Acad. Sect. A 53, 83 (1950)

  21. Robertson, H.P., Noonan T.W.: Relativity and Cosmology, W. B. Saunders Company (1969) p. 250

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Acknowledgments

This work was supported by the Spanish “Ministerio de Ciencia e Innovación”, project FIS2010-15492 and Basque Government, project IT592-13 (J. M. Aguirregabiria) and by the Spanish “Ministerio de Economía y Competitividad”, MICINN-FEDER project FIS2012-33582 (R. Lapiedra and J. A. Morales-Lladosa).

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Authors and Affiliations

  1. Theorethical Physics, University of the Basque Country (UPV/EHU), P. O. Box 644, 48080,  Bilbao, Spain

    Juan M. Aguirregabiria

  2. Departament d’Astronomia i Astrofísica, Universitat de València, E-46100,  Burjassot, València, Spain

    Ramon Lapiedra & Juan Antonio Morales-Lladosa

Authors
  1. Juan M. Aguirregabiria
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  2. Ramon Lapiedra
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  3. Juan Antonio Morales-Lladosa
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Correspondence to Juan Antonio Morales-Lladosa.

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Aguirregabiria, J.M., Lapiedra, R. & Morales-Lladosa, J.A. Stability of the intrinsic energy vanishing in the Schwarzschild metric under a slow rotation. Gen Relativ Gravit 46, 1744 (2014). https://doi.org/10.1007/s10714-014-1744-9

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  • DOI: https://doi.org/10.1007/s10714-014-1744-9

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