On the magnetohydrodynamic description of a two-component plasma in the Kerr metric

Abstract

The magnetohydrodynamic equations describing an inviscid, fully ionized plasma in the vicinity of a rotating black hole are derived from a two-component plasma theory within the framework of the 3+1 split of the Kerr metric. Of central interest is the generalized Ohm's law. In the limit of quasi-neutral plasma it contains no new terms as compared with special relativity. Gravitomagnetic terms appear in Ohm's law only if the plasma is charged in its rest frame or the magnetohydrodynamic approximation is not applied. It is argued that a relativistic single-fluid description of a multiple-component plasma is possible only for cold (i.e. intrinsically non-relativistic) components. As seen by local stationary observers, close to the horizon the electron collision time becomes longer than dynamical timescales, i.e. the plasma appears to behave as particles.