Resistive Magnetohydrodynamic Accretion Disks around Black Holes

The properties of a resistive magnetohydrodynamic (MHD) accretion disk which surrounds a black hole is discussed. A diffusion equation is obtained from general relativistic Maxwell's equations and Ohm's law under the thin-disk approximation. We find a simple solution to it that is consistent with our assumption. This solution suggests the plausible radial dependence of the accretion flow which is identical with that in the standard α-viscosity model. The rates of transfer of electromagnetic energy and angular momentum from the disk surface are calculated as well as the Ohmic dissipation rate in the disk. The former two rates are shown to have the same angular velocity dependences as derived in the force-free and ideal MHD approximations, when we use the thin-disk approximation. It is also shown that the energy flux from the disk surface is comparable to the Ohmic dissipation rate in the disk. The connection of the disk field to the external field is discussed in two extreme cases in order to illustrate the way through which the rotation of the hole can effect the above two rates. The possible application of our model to radio-loud active galactic nuclei is also discussed.