The laws of perfect general-relativistic magnetohydrodynamics (GRMHD) are rewritten in 3+1 language in a general spacetime. The laws are expressed in terms of quantities (magnetic field, flow velocity, . . .) that would be measured by the ‘‘fiducial observers’’ whose world lines are orthogonal to the hypersurfaces of constant time. This 3+1 formalism of GRMHD should be of interest in numerical relativity, numerical astrophysics, and the membrane paradigm for black holes. The GRMHD equations are also specialized to a stationary spacetime and a stationary MHD flow with one arbitrary spatial symmetry (e.g., a stationary MHD magnetosphere for a rotating Kerr black hole); and the general features of stationary, symmetric GRMHD solutions are discussed.

• Received 13 June 1988

DOI:https://doi.org/10.1103/PhysRevD.39.2933