Motion of charged particles in a NUTty Einstein–Maxwell spacetime and causality violation

  • Gérard Clément
  • Mourad Guenouche
Research Article


We investigate the motion of electrically charged test particles in spacetimes with closed timelike curves, a subset of the black hole or wormhole Reissner–Nordström-NUT spacetimes without periodic identification of time. We show that, while in the wormhole case there are closed worldlines inside a potential well, the wordlines of initially distant charged observers moving under the action of the Lorentz force can never close or self-intersect. This means that for these observers causality is preserved, which is an instance of our weak chronology protection criterion.


Einstein–Maxwell NUT Charged test particle Causality 



We thank Dmitry Gal’tsov for fruitful discussions and suggestions, and Júlio Fabris for valuable comments. MG acknowledges the support of the Ministry of Higher Education and Scientific Research of Algeria (MESRS) under Grant 0092009009.


  1. 1.
    Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)CrossRefzbMATHGoogle Scholar
  2. 2.
    Hawking, S.W.: Phys. Rev. D 46, 603 (1992)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Gödel, K.: Rev. Mod. Phys. 21, 447 (1949)ADSCrossRefGoogle Scholar
  4. 4.
    Taub, A.H.: Ann. Math. 53, 472 (1951)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Newman, E., Tamburino, L., Unti, T.: J. Math. Phys. 4, 915 (1963)ADSCrossRefGoogle Scholar
  6. 6.
    Brill, D.R.: Phys. Rev. 133, B845 (1964)ADSCrossRefGoogle Scholar
  7. 7.
    Misner, C.W.: J. Math. Phys. 4, 924 (1963)ADSCrossRefGoogle Scholar
  8. 8.
    Zimmerman, R.L., Shahir, B.Y.: Gen. Relativ. Gravit. 21, 821 (1989)ADSCrossRefGoogle Scholar
  9. 9.
    Clément, G., Gal’tsov, D., Guenouche, M.: Phys. Lett. B 750, 591 (2015). arXiv:1508.07622 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Clément, G., Gal’tsov, D., Guenouche, M.: Phys. Rev. D 93, 024048 (2016). arXiv:1509.07854 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Novello, M., Svaiter, N.F., Guimarães, M.E.X.: Gen. Relativ. Gravit. 25, 137 (1993)ADSCrossRefGoogle Scholar
  12. 12.
    Cebeci, H., Özdemir, N., Sentorun, S.: Phys. Rev. D 93, 104031 (2016). arXiv:1512.08682 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Kagramanova, V., Kunz, J., Hackmann, E., Lammerzahl, C.: Phys. Rev. D 81, 124044 (2010). arXiv:1002.4342 ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Bañados, M., Teitelboim, C., Zanelli, J.: Phys. Rev. Lett. 69, 1849 (1992). arXiv:hep-th/9204099 ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Bañados, M., Henneaux, M., Teitelboim, C., Zanelli, J.: Phys. Rev. D 48, 1506 (1993). arXiv:gr-qc/9302012 ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Moussa, K.Ait, Clément, G., Leygnac, C.: Class. Quantum Grav. 20, L277 (2003). arXiv:gr-qc/0303042 ADSCrossRefGoogle Scholar
  17. 17.
    Bouchareb, A., Clément, G.: Class. Quantum Grav. 24, 5581 (2007). arXiv:0706.0263 ADSCrossRefGoogle Scholar
  18. 18.
    Anninos, D., Li, W., Padi, M., Song, W., Strominger, A.: JHEP 0903, 130 (2009). arXiv:0807.3040 ADSCrossRefGoogle Scholar
  19. 19.
    Moussa, K.Ait, Clément, G., Guennoune, H., Leygnac, C.: Phys. Rev. D 78, 064065 (2008). [arXiv:0807.4241]ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.LAPThUniversité Savoie Mont Blanc, CNRSAnnecy-le-Vieux CedexFrance
  2. 2.Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences ExactesUniversité de Constantine 1ConstantineAlgeria
  3. 3.Department of Physics, Faculty of SciencesHassiba Benbouali University of ChlefOuled FaresAlgeria

Personalised recommendations