Magnetic field of a current loop around a Schwarzschild black hole

A multipole expansion for arbitrary quasistatic axisymmetric magnetic fields in a Schwarzschild background metric is found from Maxwell's equations in curved space-time. Using this expansion, the magnetic field of a quasistatic current loop located symmetrically around a Schwarzschild black hole is obtained. The field both inside and outside the loop is calculated, and the behavior of its dipole part is shown explicitly in certain limiting cases.