General Relativity and Gravitation

, Volume 41, Issue 9, pp 1981–2001 | Cite as

Accelerating electromagnetic magic field from the C-metric

  • Jiří BičákEmail author
  • David Kofroň
Research Article


Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the “magic field” of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr–Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the “accelerating magic field” represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born’s solution for two uniformly accelerated monopole charges.


Electromagnetic magic field Kerr–Newman solution C-metric Boost-rotation symmetric spacetimes 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bičák J., Kofroň D.: The Newtonian limit of spacetimes for accelerated particles and black holes. Gen. Relativ. Gravit 41, 153–172 (2009)zbMATHCrossRefADSGoogle Scholar
  2. 2.
    Bičák J.: Gravitational radiation from uniformly accelerated particles in general relativity. Proc. Roy. Soc. Lond. A 302, 201–224 (1968)CrossRefADSGoogle Scholar
  3. 3.
    Bičák, J.: Selected solutions of Einstein’s field equations: their role in general relativity and astrophysics. In: Schmidt, B.G. (ed.) Einstein’s Field Equations and Their Physical Implications, Selected Essays in Honour of Jürgen Ehlers. Lect. Notes Phys., vol. 540, pp. 1–112. Springer, Berlin (2000)Google Scholar
  4. 4.
    Bičák J., Muschall R.: Electromagnetic fields and radiative patterns from multipoles in hyperbolic motion. Wiss. Zeits. der Friedrich-Schiller-Universität Jena 39, 15–20 (1990)Google Scholar
  5. 5.
    Bičák, J., Pravda, V.: Spinning C metric: radiative spacetime with accelerating, rotating black holes. Phys. Rev. D 60, 044004 (1999)CrossRefADSMathSciNetGoogle Scholar
  6. 6.
    Bičák J., Schmidt B.: Asymptotically flat radiative space-times with boost-rotation symmetry: The general structure. Phys. Rev. D 40, 1827–1853 (1989)CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Bonnor W.: Closed timelike curves in general relativity. Int. J. Mod. Phys. D 12, 1705–1708 (2003)CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Bonnor W., Swaminayaran N.: An exact solution for uniformly accelerated particles in general relativity. Z. Phys. 177, 1547–1559 (1964)Google Scholar
  9. 9.
    Ehlers J.: Examples of Newtonian limits of relativistic spacetimes. Class. Quantum Grav. 14, A119–A126 (1997)zbMATHCrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Ehlers J.: Newtonian limit of general relativity. In: Francoise, J.P., Naber, G.L., Tsou, S.T.(eds) Encyclopedia of Mathematical Physics, vol. 3, pp. 503–509. Elsevier, Amsterdam (2006)CrossRefGoogle Scholar
  11. 11.
    Ehlers J., Kundt K.: Exact solutions of the gravitational field equations. In: Witten, L.(eds) Gravitation: An Introduction to Current Research, Wiley, New York (1962)Google Scholar
  12. 12.
    Griffiths J.B., Krtouš P., Podolský J.: Interpreting the C-metric. Class. Quantum Grav. 23, 6745–6766 (2006)zbMATHCrossRefADSGoogle Scholar
  13. 13.
    Griffiths J.B., Podolský J.: Global aspects of accelerating and rotating black hole spacetimes. Class. Quantum Grav. 23, 555–568 (2006)zbMATHCrossRefADSGoogle Scholar
  14. 14.
    Havrdová L., Krtouš P.: Melvin universe as a limit of the C-metric. Gen. Relativ. Gravit. 39, 291–296 (2007)zbMATHCrossRefADSGoogle Scholar
  15. 15.
    Hong K., Teo E.: A new form of the C-metric. Class. Quantum Grav. 20, 3269–3277 (2003)zbMATHCrossRefADSMathSciNetGoogle Scholar
  16. 16.
    Hong K., Teo E.: A new form of the rotating C-metric. Class. Quantum Grav. 22, 109–117 (2005)zbMATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Kinnersley W., Walker M.: Uniformly accelerating charged mass in general relativity. Phys. Rev. D 2, 1359–1370 (1970)CrossRefADSMathSciNetGoogle Scholar
  18. 18.
    Letelier P.S., de Oliveira S.R.: Double Kerr-NUT spacetimes: spinning strings and spinning rods. Phys. Lett. A 238, 101–106 (1998)zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Lynden-Bell, D.: A magic electromagnetic field. In: Thompson, M.J., Christensen-Dalsgaard, J. (eds.) Stellar Astrophysical Fluid Dynamics, pp. 369–375. Cambridge University Press, Cambridge (2003)Google Scholar
  20. 20.
    Lynden-Bell, D.: Electromagnetic magic: The relativistically rotating disk. Phys. Rev. D 70, 105017 (2004)CrossRefADSMathSciNetGoogle Scholar
  21. 21.
    Lynden-Bell, D.: Relativistically spinning charged sphere. Phys. Rev. D 70, 104021 (2004)CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    Misner C.W., Thorne K.S., Wheeler J.A.: Gravitation. W.H. Freeman and Co, New York (1973)Google Scholar
  23. 23.
    Newman E.T.: Classical, geometric origin of magnetic moments, spin-angular momentum, and the Dirac gyromagnetic ratio. Phys. Rev. D 65, 104005 (2002)CrossRefADSGoogle Scholar
  24. 24.
    Pekeris C.L., Frankowski K.: Hyperfine splitting in muonium, positronium, and hydrogen, deduced from a solution of Dirac’s equation in Kerr-Newman geometry. Phys. Rev. A 39, 518–529 (1989)CrossRefADSGoogle Scholar
  25. 25.
    Plebański J.F., Demiański M.: Rotating, charged, and uniformly accelerating mass in general relativity. Ann. Phys. 98, 98–127 (1976)zbMATHCrossRefADSGoogle Scholar
  26. 26.
    Rohrlich F.: Classical Charged Particles. World Scientific Publishing Co, Singapore (2007)zbMATHGoogle Scholar
  27. 27.
    Stephani H., Kramer D., MacCallum M., Hoensealers C., Herlt E.: Exact Solutions of Einstein’s Field Equations, 2nd edn. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  28. 28.
    Wald R.M.: General Relativity. University of Chicago Press, Chicago (1984)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institute of Theoretical Physics, Faculty of Mathematics and PhysicsCharles UniversityPrague 8Czech Republic

Personalised recommendations