Abstract
We modify and generalize the known solution for the electromagnetic field when a vacuum, stationary, axisymmetric black hole is immersed in a uniform magnetic field to the case of nonvacuum black holes (of modified gravity) and determine all linear terms of the vector potential in powers of the magnetic field and the rotation parameter.
Highlights
Is endowed with the property of being parallel, that is, proportional, to some vector potential less
In Ref. [1], this property was employed as an ansatz to determine the electromagnetic field of a vacuum, stationary, axisymmetric, asymptotically flat black hole placed in a uniform magnetic field that is asymptotically parallel to the axis of symmetry
We have derived expressions for the vector potential and electromagnetic field of a rotating and nonrotating charged black hole immersed in a uniform magnetic field
Summary
[1], this property was employed as an ansatz to determine the electromagnetic field of a vacuum, stationary, axisymmetric, asymptotically flat black hole placed in a uniform magnetic field that is asymptotically parallel to the axis of symmetry. As far as Q is considered as a perturbation, the potential given by (1) and (3) remains a good approximation for many astrophysical purposes This fails to be the case if one is interested in the accretion phenomena that take place in the vicinity of the innermost stable circular orbit (ISCO) whose radius approaches that of the event horizon, for there the currents (J t , J φ) cannot be neglected. One of the purposes of this paper is to provide an “exact” formula for the vector potential of a vacuum charged black hole immersed in a uniform magnetic field parallel to its axis of symmetry. The purpose extends to include nonvacuum charged and uncharged black holes
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