Generation of magnetic fields by a gravitomagnetic plasma battery

The generation of magnetic fields by a battery, operating in an ion-electron plasma around a Kerr black hole, is studied in the 3+1 split of the Kerr metric. It is found that the gravitomagnetic contributions to the electron partial pressure are able to drive currents. The strength of the equilibrium magnetic field should be higher than for the classical Biermann battery, which is found to operate in this relativistic context as well, since the gravitomagnetic driving terms can less easily be quenched than the classical ones. In axisymmetry the battery can induce only toroidal magnetic fields. Once a toroidal magnetic field is present, however, the coupling of gravitomagnetic and electromagnetic fields generates a poloidal magnetic field even in axisymmetry. A rotating black hole, embedded in plasma, will therefore always generate toroidal and poloidal magnetic fields.