  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 (Khanna & Camenzind 1996a,b). A rotating black hole, embedded in
plasma, will therefore always generate toroidal and poloidal magnetic fields.

Astrophysics;General Relativity and Quantum Cosmology;Plasma Physics