Stationary Electromagnetic Fields of a Slowly Rotating Magnetized Neutron Star in General Relativity


Following the general formalism presented by Rezzolla, Ahmedov and Miller,(1) we here derive analytic solutions of the electromagnetic fields equations in the internal and external background spacetime of a slowly rotating highly conducting magnetized neutron star. The star is assumed to be isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. Our results indicate that the electromagnetic fields of a slowly rotating neutron star are modified by general relativistic effects arising from both the monopolar and the dipolar parts of the gravitational field. The results presented here differ from the ones discussed by Rezzolla, Ahmedov and Miller(1) mainly in that we here consider the interior magnetic field to be dipolar with the same radial dependence as the external one. While this assumption might not be a realistic one, it should be seen as the application of our formalism to a case often discussed in the literature.

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  1. 1.

    L. Rezzolla, B. J. Ahmedov, and J. C. Miller, “General relativistic electromagnetic fields of a slowly rotating magnetized neutron star. I. Formulation of the equations,” Mon. Not. R. Astr. Soc. 322, 723 (2001).

    Google Scholar 

  2. 2.

    V. L. Ginzburg and L. M. Ozernoy, “On gravitational collapse of magnetic stars,” Zh. Eksp. Teor. Fiz. 47, 1030–1040 (1964).

    Google Scholar 

  3. 3.

    J. L. Anderson and J. M. Cohen, “Gravitational collapse of magnetic neutron stars,” Astrophys. Space Science 9, 146–152 (1970).

    Google Scholar 

  4. 4.

    J. A. Petterson, “Magnetic field of a current loop around a Schwarzschild black hole,” Phys. Rev. D 10, 3166–3170 (1974); “Stationary axisymmetric electromagnetic fields around a rotating black hole,” Phys. Rev. D 12, 2218–2225 (1975).

    Google Scholar 

  5. 5.

    U. Geppert, D. Page, and T. Zannias, “Magnetic field decay in neutron stars. Analysis of general relativistic effects,” Phys. Rev. D 61, 123004 (2000).

    Google Scholar 

  6. 6.

    A. Muslimov and A. I. Tsygan, “General relativistic potential drops above pulsar polar caps,” Mon. Not. R. Astr. Soc. 255, 61–70 (1992).

    Google Scholar 

  7. 7.

    A. Muslimov and A. K. Harding, “Towards the quasi-steady state electrodynamics of a neutron star,” Astrophys. J. 485, 735–746 (1997).

    Google Scholar 

  8. 8.

    K. Konno and Ya. Kojima, “General relativistic modification of a pulsar electromagnetic yield,” Prog. Theor. Phys. 104, 1117–1127 (2000).

    Google Scholar 

  9. 9.

    J. B. Hartle, “Slowly rotating relativistic stars. I. Equations of structure,” Astrophys. J. 150, 1005–1029 (1967).

    Google Scholar 

  10. 10.

    J. B. Hartle and K. S. Thorne, “Slowly rotating relativistic stars. II. Models for neutron stars and supermassive stars,” Astrophys. J. 153, 807–834 (1968).

    Google Scholar 

  11. 11.

    L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1971).

    Google Scholar 

  12. 12.

    J. C. Miller, “Quasi-stationary gravitational collapse of slowly rotating bodies in general relativity,” Mon. Not. R. Astr. Soc. 179, 483–498 (1977).

    Google Scholar 

  13. 13.

    S. Sengupta, “General relativistic effects on the induced electric field exterior to pulsars,” Astrophys. J. 449, 224–230 (1995).

    Google Scholar 

  14. 14.

    S. Sengupta, “General relativistic effects on the ohmic decay of crustal magnetic fields,” Astrophys. J. 479, L133–L136 (1997).

    Google Scholar 

  15. 15.

    B. J. Ahmedov, “General relativistic galvano-gravitomagnetic effect in current carrying conductors,” Phys. Lett. A 256, 9–14 (1999).

    Google Scholar 

  16. 16.

    A. Lichnerowicz, Relativistic Hydrodynamics and Magnetohydrodynamics (Benjamin, New York, 1967).

    Google Scholar 

  17. 17.

    G. F. R. Ellis, “Relativistic cosmology,'' in Cargese Lectures in Physics, Vol. 6, E. Schatzman, ed. (Gordon & Breach, 1973), pp. 1–60.

  18. 18.

    H. Stephani, General Relativity (University Press, Cambridge, 1990).

    Google Scholar 

  19. 19.

    J. M. Bardeen, W. H. Press, and S. A. Teukolsky, “Rotating black holes: Locally non-rotating frames, Energy Extraction, and Scalar Synchrotron Radiation,” Astrophys. J. 178, 347–369 (1972).

    Google Scholar 

  20. 20.

    A. J. Deutsch, “The electromagnetic field of an idealized star in rigid rotation in vacuo,” Ann. Astrophys. 1, 1–10 (1955).

    Google Scholar 

  21. 21.

    A. Gupta, A. Mishra, H. Mishra, and A. R. Prasanna, “Rotating compact objects with magnetic fields,” Class. Quantum Grav. 15, 3131–3145 (1998).

    Google Scholar 

  22. 22.

    A. R. Prasanna and A. Gupta, “Structure of external electromagnetic field around a slowly rotating compact object and charged-particle trajectories,” Nuovo Cimento B 112, 1089–1106 (1997).

    Google Scholar 

  23. 23.

    A. Jeffrey, Handbook of Mathematical Formulas and Integrals (Academic, San Diego, 1995).

    Google Scholar 

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Rezzolla, L., Ahmedov, B.J. & Miller, J.C. Stationary Electromagnetic Fields of a Slowly Rotating Magnetized Neutron Star in General Relativity. Foundations of Physics 31, 1051–1065 (2001).

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  • Magnetic Field
  • Electromagnetic Field
  • Neutron Star
  • Field Equation
  • Gravitational Field