Advertisement

General Relativity and Gravitation

, Volume 40, Issue 6, pp 1203–1217 | Cite as

Nonlinear gravito-electromagnetism

  • Roy Maartens
Research Article

Abstract

There is a non-linear and covariant electromagnetic analogy for gravity, in which the full Bianchi identities are Maxwell-type equations for the free gravitational field, encoded in the Weyl tensor. This tensor gravito-electromagnetism is based on a covariant generalization of spatial vector algebra and calculus to spatial tensor fields, and includes all non-linear effects from the gravitational field and matter sources. The non-linear vacuum Bianchi equations are invariant under spatial duality rotation of the gravito-electric and gravito-magnetic tensor fields. The super-energy density and super-Poynting vector of the gravitational field are natural duality invariants, and satisfy a super-energy conservation equation.

Keywords

General relativity Electromagnetism 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Mashhoon, B.: Gravitoelectromagnetism: A Brief Review. arXiv:gr-qc/0311030Google Scholar
  2. 2.
    Cohen, J.M., Mashhoon, B.: Phys. Lett. A 181, 353 (1993)CrossRefADSGoogle Scholar
  3. 3.
    Mashhoon, B., Gronwald, F., Hehl, F.W., Theiss, D.S.: Annalen Phys. 8, 135 (1999). [arXiv:gr-qc/9804008]MATHCrossRefADSGoogle Scholar
  4. 4.
    Mashhoon, B., McClune, J.C., Quevedo, H.: Class. Quant. Grav. 16, 1137 (1999). [arXiv:gr-qc/9805093]MATHCrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Mashhoon, B., Gronwald, F., Lichtenegger, H.I.M.: Lect. Notes Phys. 562, 83 (2001). [arXiv:gr-qc/9912027]ADSCrossRefGoogle Scholar
  6. 6.
    Bini, D., Jantzen, R.T., Mashhoon, B.: Class. Quant. Grav. 18, 653 (2001). [arXiv:gr-qc/0012065]MATHCrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Mashhoon, B., Iorio, L., Lichtenegger, H.: Phys. Lett. A 292, 49 (2001). [arXiv:gr-qc/0110055]MATHCrossRefADSGoogle Scholar
  8. 8.
    Lichtenegger, H.I.M., Iorio, L., Mashhoon, B.: Annalen Phys. 15, 868 (2006). [arXiv:gr-qc/0211108]MATHCrossRefADSGoogle Scholar
  9. 9.
    Maartens, R., Mashhoon, B., Matravers, D.R.: Class. Quant. Grav. 19, 195 (2002). [arXiv:gr-qc/0104049]MATHCrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Bini, D., Jantzen, R.T., Mashhoon, B.: Class. Quant. Grav. 19, 17 (2002). [arXiv:gr-qc/0111028]MATHCrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Trümper, M.: unpublished (see [15])Google Scholar
  12. 12.
    Kundt, W., Trümper, M.: Akad. Wiss. Lit. Mainz Abh. Math. Naturwiss. Kl. 12, 1 (1962)Google Scholar
  13. 13.
    Ehlers, J.: Gen. Rel. Grav. 25, 1225 (1993). (translation of 1961 article)MATHCrossRefADSMathSciNetGoogle Scholar
  14. 14.
    Hawking, S.W.: Astrophys. J. 145, 544 (1966)CrossRefADSGoogle Scholar
  15. 15.
    Ellis, G.F.R.: In: Sachs, R.K. (ed) General Relativity and Cosmology. Academic, New York (1971)Google Scholar
  16. 16.
    Maartens, R., Bassett, B.A.: Class. Quant. Grav. 15, 705 (1998). [arXiv:gr-qc/9704059]MATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Matte, A.: Can. J. Math. 5, 1 (1953)MATHMathSciNetGoogle Scholar
  18. 18.
    Pirani, F.: Phys. Rev. 105, 1089 (1957)MATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Bel, L.: C. R. Acad. Sci. 247, 1094 (1958)MATHMathSciNetGoogle Scholar
  20. 20.
    Bel, L.: Gen. Rel. Grav. 32, 2047 (2000). (translation of 1962 article)MATHCrossRefADSMathSciNetGoogle Scholar
  21. 21.
    Penrose, R.: Ann. Phys. 10, 171 (1960)MATHCrossRefADSMathSciNetGoogle Scholar
  22. 22.
    Zakharov, V.D.: Gravitational Waves in Einstein’s Theory. Halsted, New York (1973)MATHGoogle Scholar
  23. 23.
    Jantzen, R.T., Carini, P., Bini, D.: Annals Phys. 215, 1 (1992). [arXiv:gr-qc/0106043]CrossRefADSMathSciNetGoogle Scholar
  24. 24.
    Maartens, R.: Phys. Rev. D 55, 463 (1997). [arXiv:astro-ph/9609198]CrossRefADSMathSciNetGoogle Scholar
  25. 25.
    van Elst, H.: Ph.D. thesis, University of London (1996)Google Scholar
  26. 26.
    Maartens, R., Ellis, G.F.R., Siklos, S.T.C.: Class. Quant. Grav. 14, 1927 (1997). [arXiv:gr-qc/9611003]MATHCrossRefADSMathSciNetGoogle Scholar
  27. 27.
    Challinor, A., Lasenby, A.: Astrophys. J. 513, 1 (1999). [arXiv:astro-ph/9804301]CrossRefADSGoogle Scholar
  28. 28.
    Maartens, R., Gebbie, T., Ellis, G.F.R.: Phys. Rev. D 59, 083506 (1999). [arXiv:astro-ph/9808163]CrossRefADSGoogle Scholar
  29. 29.
    MacCallum, M.A.H.: Integrability in tetrad formalisms and conservation in cosmology. arXiv:gr-qc/9806003Google Scholar
  30. 30.
    Ellis, G.F.R., van Elst, H.: Cosmological models. arXiv:gr-qc/9812046Google Scholar
  31. 31.
    Tsagas, C.G., Challinor, A., Maartens, R.: Relativistic cosmology and large-scale structure. arXiv: 0705.4397 [astro-ph]Google Scholar
  32. 32.
    Ellis, G.F.R.: In: Schatzman, E. (ed.) Cargése Lectures in Physics, vol. VI. Gordon and Breach, New York (1973)Google Scholar
  33. 33.
    Gomez-Lobo, A.P.: Dynamical laws of superenergy in General Relativity. arXiv:0707.1475 [gr-qc]Google Scholar
  34. 34.
    Mashhoon, B., McClune, J.C., Quevedo, H.: Phys. Lett. A 231, 47 (1997). [arXiv:gr-qc/9609018]MATHCrossRefADSMathSciNetGoogle Scholar
  35. 35.
    Senovilla, J.M.M.: Class. Quant. Grav. 17, 2799 (2000). [arXiv:gr-qc/9906087]MATHCrossRefADSMathSciNetGoogle Scholar
  36. 36.
    Senovilla, J.M.M.: General electric-magnetic decomposition of fields, positivity and Rainich-like conditions. arXiv:gr-qc/0010095Google Scholar
  37. 37.
    Kramer, D., Stephani, H., MacCallum, M.A.H., Herlt, E.: Exact Solutions of Einstein’s Field Equations. Cambridge University Press, Cambridge (1980)MATHGoogle Scholar
  38. 38.
    Bonnor, W.B.: Class. Quant. Grav. 12, 499, 1483 (1995).Google Scholar
  39. 39.
    Edgar, S.B., Senovilla, J.M.M.: Class. Quant. Grav. 21, L133 (2004). [arXiv:gr-qc/0408071]MATHCrossRefADSMathSciNetGoogle Scholar
  40. 40.
    Dunsby, P.K.S., Bassett, B.A.C., Ellis, G.F.R.: Class. Quant. Grav. 14, 1215 (1997). [arXiv:gr-qc/9811092]MATHCrossRefADSMathSciNetGoogle Scholar
  41. 41.
    Challinor, A.: Class. Quant. Grav. 17, 871 (2000). [arXiv:astro-ph/9906474]MATHCrossRefADSMathSciNetGoogle Scholar
  42. 42.
    Tilley, D., Maartens, R.: Class. Quant. Grav. 17, 2875 (2000). [arXiv:gr-qc/0002089]MATHCrossRefADSMathSciNetGoogle Scholar
  43. 43.
    Marklund, M., Dunsby, P.K.S., Brodin, G.: Phys. Rev. D 62, 101501 (2000). [arXiv:gr-qc/0007035]CrossRefADSGoogle Scholar
  44. 44.
    Tsagas, C.G.: Class. Quant. Grav. 19, 3709 (2002). [arXiv:gr-qc/0202095]MATHCrossRefADSMathSciNetGoogle Scholar
  45. 45.
    Bruni, M., Matarrese, S., Pantano, O.: Astrophys. J. 445, 958 (1995). [arXiv:astro-ph/9406068]CrossRefADSGoogle Scholar
  46. 46.
    van Elst, H., Uggla, C., Lesame, W.M., Ellis, G.F.R., Maartens, R.: Class. Quant. Grav. 14, 1151 (1997). [arXiv:gr-qc/9611002]MATHCrossRefADSGoogle Scholar
  47. 47.
    Maartens, R., Lesame, W.M., Ellis, G.F.R.: Class. Quant. Grav. 15, 1005 (1998). [arXiv:gr-qc/9802014]MATHCrossRefADSMathSciNetGoogle Scholar
  48. 48.
    Sopuerta, C.F., Maartens, R., Ellis, G.F.R., Lesame, W.M.: Phys. Rev. D 60, 024006 (1999). [arXiv: gr-qc/9809085]CrossRefADSMathSciNetGoogle Scholar
  49. 49.
    Van den Bergh, N., Wylleman, L.: Class. Quant. Grav. 21, 2291 (2004). [arXiv:gr-qc/0402125]MATHCrossRefADSGoogle Scholar
  50. 50.
    Wylleman, L.: Class. Quant. Grav. 23, 2727 (2006). [arXiv:gr-qc/0601142]MATHCrossRefMathSciNetGoogle Scholar
  51. 51.
    Wylleman, L., Van den Bergh, N.: Phys. Rev. D 74, 084001 (2006). [arXiv:gr-qc/0604025]CrossRefADSGoogle Scholar
  52. 52.
    Wylleman, L., Van den Bergh, N.: J. Phys. Conf. Ser. 66, 012025 (2007)CrossRefADSGoogle Scholar
  53. 53.
    Bastiaensen, B., Karimian, H.R., Van den Bergh, N., Wylleman, L.: Class. Quant. Grav. 24, 3211 (2007). [arXiv:gr-qc/0703022]MATHCrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institute of Cosmology and GravitationUniversity of PortsmouthPortsmouthUK

Personalised recommendations