LAUSR

To study time-dependent phenomena of plasma surrounding a non-rotating black hole with a dipolar magnetic field, we have developed a fully set of 3+1 formalism of generalised general relativistic magnetohydrodynamic (GRMHD) equations. The general relativistic phenomena, in particular, have been investigated with respect to the Ohm law. Magnetofluid is supposed to flow in three directions and forms a thick disc structure around the central black hole. All physical quantities of the system are functions of three variables: radial distance r, polar angle θ and time t. The radial, meridional and time behaviors of all these quantities have been investigated. It has been shown that the electrical conductivity of the fluid is not constant and may be both positive and negative depending on the values of some free parameters. The initially purely rotating non-magnetized plasma in the presence of an external magnetic field gives rise to an azimuthal current density and a charge density measured by the comoving observer. This current generates an electromagnetic field inside the disc which has both poloidal and toroidal components. The dipolar magnetic field lines of the central black hole is able to penetrate the plasma disc, due to the presence of a finite resistivity for the plama. The accreting plasma pushes them outwards and makes them parallel to the rotation axis of the disc in the meridional plane.