Potential equations for plasmas round a rotating black hole -: art. no. 044007

The generalized Helmholtz equations of relativistic multifluid plasmas can be integrated fur axisymmetric equilibria in close analogy to the magnetic flux conservation law in ideal magnetohydrodynamics [J. D. Bekenstein and E. Oron, Phys. Rev. D 18, 1809 (1978)]. The results are, for each fluid component, two Aux functions and a potential equation for the poloidal stream function. Ampere's equation for the four-potential A(nu), is reduced to two coupled equations for the time-like and the toroidal component. So we have altogether four potential equations for a two-component plasma; they can he derived from a variational principle.