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General Relativity and Gravitation

, Volume 44, Issue 7, pp 1657–1675 | Cite as

A relativistic generalisation of rigid motions

  • J. Llosa
  • A. Molina
  • D. Soler
Research Article

Abstract

A weaker substitute for the too restrictive class of Born-rigid motions is proposed, which we call radar-holonomic motions. The definition is expressed as a set of differential equations. Integrability conditions and Cauchy problem are studied. We finally obtain an example of a radar-holonomic congruence containing a given worldline with a given value of the rotation on this line.

Keywords

Rigid motions Congruences of world lines Strain rate tensor Radar metric 

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References

  1. 1.
    Audretsch J., Marzlin K.P.: Phys. Rev. A 50, 2080 (1994)ADSCrossRefGoogle Scholar
  2. 2.
    Ni W.T., Zimmermann M.: Phys. Rev. D 17, 1473 (1978)ADSCrossRefGoogle Scholar
  3. 3.
    Bel L1., Martín J., Molina A.: J. Phys. Soc. Jpn. 63, 4350 (1994)ADSMATHCrossRefGoogle Scholar
  4. 4.
    Zel’manov A.: Sov. Phys. Dokl. 1, 227 (1956)ADSMATHGoogle Scholar
  5. 5.
    Cattaneo C.: Ann. Mat. Pura Appl. 48, 361 (1959)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Ehlers J.: Gen. Relativ. Gravit. 25, 1225 (1993)MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    Born M.: Phys. Z. 10, 814 (1909)Google Scholar
  8. 8.
    Herglotz G.: Ann. Phys. Lpz. 31, 393 (1910)ADSMATHCrossRefGoogle Scholar
  9. 9.
    Noether F.: Ann. Phys. Lpz. 31, 919 (1910)ADSMATHCrossRefGoogle Scholar
  10. 10.
    Llosa J.: Class. Quantum Gravity 14, 165 (1997)MathSciNetADSMATHCrossRefGoogle Scholar
  11. 11.
    Bel Ll., Llosa J.: Gen. Relativ. Gravit. 27, 1089 (1995)MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    Deturk D.M., Yang D.: Duke Math. J. 51, 243 (1984)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Bel Ll., Coll B.: Gen. Relativ. Gravit. 25, 613 (1993)MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    Choquet-Bruhat Y., Dewitt-Morette C., Dillard-Bleick M.: Analysis, Manifolds and Physics, p. 308, Revised Edition. North-Holland, Amsterdam (1987)Google Scholar
  15. 15.
    John, F.: Partial Differential Equations. p. 56 Springer, New York, NY (1971)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Dept. Física FonamentalUniversitat de BarcelonaBarcelonaSpain
  2. 2.Mechanical and Industrial Production Dept.Mondragon UnibertsitateaMondragonSpain

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