In the Introduction we briefly recall our previous results on stationary electromagnetic fields on black hole backgrounds and the use of spin-weighted spherical harmonics. We then discuss static electric and magnetic test fields in a Schwarzschild background using some of these results. As sources we do not consider point charges or current loops like in previous works, rather, we analyze spherical shells with smooth electric or magnetic charge distributions as well as electric or magnetic dipole distributions depending on both angular coordinates. Particular attention is paid to the discontinuities of the field, of the 4-potential, and their relation to the source.
Electrostatics in curved backgrounds Monopole and dipole layers
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Goldberg J.N.: Conservation of the Newman-Penrose conserved quantities. Phys. Rev. Lett. 28(21), 1400 (1972)ADSCrossRefGoogle Scholar
Teukolsky S.A.: Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations. Astrophys. J. 185, 635 (1973)MathSciNetADSCrossRefGoogle Scholar
Bičák J., Dvořák L.: Stationary electromagnetic fields around black holes. I. General solutions and the fields of some special sources near a Schwarzschild black hole. Czech. J. Phys. 27, 127 (1977)ADSCrossRefGoogle Scholar
Bičák J., Dvořák L.: Stationary electromagnetic fields around black holes. II. General solutions and the fields of some special sources near a Kerr black hole. Gen. Relativ. Gravit. 7, 959 (1976)ADSCrossRefGoogle Scholar
Bičák J.: On the theories of the interacting perturbations of the Reissner-Nordström black hole. Czech. J. Phys. 29, 945 (1979)ADSCrossRefGoogle Scholar
Bičák J., Dvořák L.: Stationary electromagnetic fields around black holes. III. General solutions and the fields of current loops near the Reissner-Nordström black hole. Phys. Rev. D 22, 2933 (1980)ADSCrossRefGoogle Scholar
Bičák J., Stuchlík Z., Šob M.: Scalar fields around a charged, rotating black hole. Czech. J. Phys. 28, 121 (1978)ADSCrossRefGoogle Scholar