The flow of magnetized plasma is governed by a large number of coupled equations (Maxwell's, Euler's, conservation of energy and of baryon number) so that the solution of a problem in general-relativistic magnetohydrodynamics is very complicated, even if symmetries are present. We present here a number of new conservation laws which make the solution process easier. We obtain the general criteria for a flux conservation law to exist. We apply them to obtain the relativistic versions of the conservation of magnetic flux and of Kelvin's circulation theorem for an unmagnetized fluid, as well as a new flux conservation law for a charged fluid. For stationary and axial symmetry we find conservation laws for each component of the Maxwell tensor; these are valid even if the plasma is nonperfect. For perfect plasma we find magnetic generalizations of the relativistic Bernoulli theorems for an unmagnetized fluid. We also find a new conservation law without previous analog. As an application of our results we show that extraction of rotational energy from a black hole by interaction with a magnetized plasma is not possible in the stationary state. This contradicts previous conclusions based on the approximation of geodesic flow. Finally, still for stationary and axial symmetry, we find the magnetic generalization of Kelvin's circulation theorem. With its help we reduce the problem of solving for the field of flow and for the magnetic field to the solution of two equations: baryon conservation and a Hamilton-Jacobi-type equation. A by-product of our derivations is an explicit formula for the strength of the magnetic field in terms of fluid variables.T h e r e a r e a number of astrophysical situations in which general-relativistic magnetohydrodynamic (GRM) effects may be important. Neutron s t a r s such a s a r e found in pulsars and in s o m e of the compact x-ray s o u r c e s a r e composed of strongly magnetized degenerate plasma subject t o strong gravitational fields. The magnetosphere of such a neutron s t a r i s again a highly conducting plasma entrained in the s t a r ' s magnetic field and, in r egions close to the s t a r , subject t o i t s strong gravitational field. In the environment of a n accreting black hole, such a s may exist in s o m e of the xray s o u r c e s and in q u a s a r s , plasma carrying a frozen-in magnetic field falls in the.strong gravitational field of the hole. The relevance of GRM t o astrophysics i s thus clear.The equations of GRM have been developed over the y e a r s by a number of pe0p1e.l'~ Unfortunately there has been a s yet little application of these t o astrophysical calculations. F o r example, pulsar magnetospheres a r e still treated by special relativity.' Accretion onto black holes h a s been treated by general relativity, but in the approximation of geodesic motion which neglects magnetic E~r c e s .~*~ It appears that this trend resulted from the lack of conservation laws in GRM which might have made interesting calculations tractable. In this paper we present a num...

We study the interior magnetohydrodynamic structure of a rotating stationary axisymmetric neutron star. We assume the fluid is ideal, infinitely conducting, and flows only azimuthaly. We justify this assumption by considering in detail the superfluid physics in the interior. We obtain some of our results by taking a certain limit of previously discovered magnetohydrodynamic conservation laws. We show that the angular velocity, electric and magnetic potentials, and the red-shifted chemical potential are constant on magnetic surfaces. We demonstrate that the absence of meridional circulation implies the vanishing of the toriodal magnetic field. This clashes with previous arguments from the probable evolution of the magnetic field during the collapse to the neutron star. We solve completely Maxwell's equations for the distribution of magnetic field strength, and we show that the magnetic surfaces are the equipotentials of a simple geometrical invariant. With neglect of gravitational effects the magnetic field must be uniform in the interior in accordance with the Deutsch model, but at variance with numerous other models which have been proposed for ordinary stars. Gravitation causes the magnetic surfaces to flare out toward the polar regions and enhances the central field as compared to the polar field. The star must be charged; the charge distribution depends on the magnetic field strength and on the angular velocity relative to the local inertial frames.