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General relativistic electromagnetic fields of a slowly rotating magnetized neutron star – I. Formulation of the equations
Authors:L Rezzolla  B J Ahmedov  J C Miller
Institution:SISSA, International School for Advanced Studies, Via Beirut 2-4, 34014 Trieste, Italy;AS-ICTP, The Abdus Salam International Centre for Theoretical Physics, 34014 Trieste, Italy;Institute of Nuclear Physics, Ulughbek, Tashkent 702132, Uzbekistan;Nuclear and Astrophysics Laboratory, University of Oxford, Keble Road, Oxford OX1 3RH
Abstract:We present analytic solutions of Maxwell equations in the internal and external background space–time of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. With respect to a flat space–time solution, general relativity introduces corrections related both to the monopolar and the dipolar parts of the gravitational field. In particular, we show that in the case of infinite electrical conductivity general relativistic corrections resulting from the dragging of reference frames are present, but only in the expression for the electric field. In the case of finite electrical conductivity, however, corrections resulting from both the space–time curvature and the dragging of reference frames are shown to be present in the induction equation. These corrections could be relevant for the evolution of the magnetic fields of pulsars and magnetars. The solutions found, while obtained through some simplifying assumption, reflect a rather general physical configuration and could therefore be used in a variety of astrophysical situations.
Keywords:MHD  relativity  stars: magnetic fields  stars: neutron  stars: rotation
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