General Relativity and Gravitation

, Volume 39, Issue 9, pp 1477–1487 | Cite as

Quasi-Maxwell interpretation of the spin–curvature coupling

Research Article


We write the Mathisson-Papapetrou equations of motion for a spinning particle in a stationary spacetime using the quasi-Maxwell formalism and give an interpretation of the coupling between spin and curvature. The formalism is then used to compute equilibrium positions for spinning particles in the NUT spacetime.


Angular Momentum Equilibrium Position Magnetic Dipole Stationary Observer Supplementary Condition 
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  1. 1.
    Anandan J., Dadhich N. and Singh P. (2003). Action principle formulation for the motion of extended bodies in general relativity. Phys. Rev. D 68: 124014CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Anderson M. (2000). On stationary vacuum solutions to the Einstein equations. Ann. Henri Poincare 1: 977–994 MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bini D., de Felice F. and Geralico A. (2004a). Spinning test particles and clock effect in Kerr spacetime. Class. Quant. Grav. 21: 5441–5456 MATHCrossRefADSGoogle Scholar
  4. 4.
    Bini D., de Felice F. and Geralico A. (2004b). Spinning test particles and clock effect in Schwarzschild spacetime. Class. Quant. Grav. 21: 5427–5440 MATHCrossRefADSGoogle Scholar
  5. 5.
    Beiglböck.: the center-of-mass in Einstein’s theory of gravitation. Commun. Math. Phys. 5, 106–130 (1967)MATHCrossRefADSGoogle Scholar
  6. 6.
    Beig R. and Schmidt B. (2000). Time-independent gravitational fields. Lect. Notes Phys. 540: 325–372 ADSCrossRefMathSciNetGoogle Scholar
  7. 7.
    Costa J. and Natário J. (2005). Homogeneous cosmologies from the quasi-Maxwell formalism. J. Math. Phys. 46: 082501 CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    de Felice F. and Clarke J. (1995). Relativity on Curved Manifolds. Cambridge University Press, LondonGoogle Scholar
  9. 9.
    Dixon W. (1970). Dynamics of extended bodies in general relativity i. Momentum and angular momentum. Proc. R. Soc. Lond. A 314: 499ADSMathSciNetGoogle Scholar
  10. 10.
    Embacher F. (1984). The analog of electric and magnetic fields in stationary gravitational systems. Found. Phys. 14: 721–738CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Hartl N. (2003). Dynamics of spinning test particles in Kerr spacetime. Phys. Rev. D 67: 024005 CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Jackson J. (1998). Classical Electrodynamics. Wiley, New YorkGoogle Scholar
  13. 13.
    Künzle H. (1972). Canonical dynamics of spinning particles in gravitational and electromagnetic fields. J. Math. Phys. 13: 739–744 MATHCrossRefADSGoogle Scholar
  14. 14.
    Lynden-Bell D. and Nouri-Zonoz M. (1998). Classical monopoles: Newton, NUT-space, gravomagnetic lensing and atomic spectra. Rev. Mod. Phys. 70: 427–446 CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    Landau L. and Lifshitz E. (1997). The Classical Theory of Fields. Butterworth-Heinemann, LondonGoogle Scholar
  16. 16.
    Mathisson M. (1937). Neue mechanik materieller systeme. Acta Physiol. Pol. 6: 163–200 MATHGoogle Scholar
  17. 17.
    Mashhoon B. and Singh D. (2006). Dynamics of extended spinning masses in a gravitational field. Phys. Rev. D 74: 124006CrossRefADSGoogle Scholar
  18. 18.
    Misner C., Thorne K. and Wheeler J.A. (1973). Gravitation. Freeman, San FransiscoGoogle Scholar
  19. 19.
    Newman E., Tamburino L. and Unti T. (1963). Empty-space generalization of the Schwarzschild metric. J. Math. Phys. 4: 915–923MATHCrossRefADSMathSciNetGoogle Scholar
  20. 20.
    Nouri-Zonoz M. (1997). Cylindrical analogue of NUT space: spacetime of a line gravomagnetic monopole. Class. Quant. Grav. 14: 3123–3129MATHCrossRefADSMathSciNetGoogle Scholar
  21. 21.
    Oliva W. (2002). Geometric mechanics. Springer, HeidelbergMATHGoogle Scholar
  22. 22.
    Papapetrou A. (1951). Spinning test particles in general relativity i. Proc. R. Soc. Lond. A 209: 248MATHADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Pirani F. (1956). On the physical significance of the Riemann tensor. Acta Physiol. Pol. 15: 389–405 MathSciNetGoogle Scholar
  24. 24.
    Schattner R. (1979a). The center of mass in general relativity. Gen. Relativ. Gravit. 10(5): 377–393CrossRefADSMathSciNetGoogle Scholar
  25. 25.
    Schattner R. (1979b). The uniqueness of the center of mass in general relativity. Gen. Relativ. Gravit. 10(5): 395–399CrossRefADSMathSciNetGoogle Scholar
  26. 26.
    Semerák (1999). Spinning test particles in a Kerr field - i. Mont. Not. Astron. Soc. 308: 863–875CrossRefADSGoogle Scholar
  27. 27.
    Singh D. (2005). The dynamics of a classical spinning particle in Vaidya space-time. Phys. Rev. D 72: 084033 CrossRefADSMathSciNetGoogle Scholar
  28. 28.
    Stuchlik Z. and Kovar J. (2006). Equilibrium conditions of spinning test particles in Kerr-de Sitter spacetimes. Class. Quant. Grav. 23: 3935–3949 MATHCrossRefADSMathSciNetGoogle Scholar
  29. 29.
    Stephani H., Kramer D., MacCallum M., Hoensalaers C. and Herlt E. (2003). Exact Solutions of Einstein’s Field Equations. Cambridge University Press, London MATHGoogle Scholar
  30. 30.
    Suzuki S. and Maeda K. (1996). Chaos in Schwarzschild space-time: the motion of a spinning particle. Phys. Rev. D 55: 4848–4859 CrossRefADSGoogle Scholar
  31. 31.
    Stephani H. (2004). Relativity. Cambridge University Press, LondonGoogle Scholar
  32. 32.
    Tod K., de Felice F. and Calvani M. (1976). Spinning test particles in the field of a black hole. Nuovo Cim. B 34: 365 ADSGoogle Scholar
  33. 33.
    Tulczyjew W. (1959). Motion of multipole particles in general relativity theory. Acta Physiol. Pol. 18: 393–409 MATHMathSciNetGoogle Scholar
  34. 34.
    Wald R. (1972). Gravitational spin interaction. Phys. Rev. D 6(2): 406–413CrossRefADSGoogle Scholar
  35. 35.
    Wald R. (1984). General Relativity. University of Chicago Press, ChicagoMATHGoogle Scholar

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsInstituto Superior TécnicoLisbonPortugal

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