A note on magnetic generalizations of the Kerr and Kerr–Newman solutions

Abstract

A concise form of the asymptotically flat metrics describing the simplest magnetic generalizations of the Kerr and Kerr–Newman spacetimes is presented. The explicit formulae for the corresponding electromagnetic potentials are also given, together with simple expressions of all metric functions in the equatorial plane. It is shown that the magnetic field changes the structure of the gravitational multipole moments of the vacuum Kerr solution.

Metric of a rotating charged magnetized sphere

“…so that we have fully described the gravitational and electromagnetic fields of the rotating sphere carrying both the electric charge and magnetic dipole moment. Evidently, due to its finite multipole structure, the 4-parameter solution ( 9)-( 12) does not contain the Kerr and KN spacetimes as particular cases, and therefore it differs from the 4-parameter solution describing the magnetized KN source [16,17]. However, in the limit of zero angular momentum (j = 0), both solutions coincide, representing a magnetized Reissner-Nordström mass.…”