Resistive accretion flows around a Kerr black hole

In this paper, we present the stationary axisymmetric configuration of a resistive magnetised thick accretion disc in the vicinity of external gravity and intrinsic dipolar magnetic field of a slowly rotating black hole. The plasma is described by the equations of fully general relativistic magnetohydrodynamics (MHD) along with the Ohm's law and in the absence of the effects of radiation fields. We try to solve these two-dimensional MHD equations analytically as much as possible. However, we sometimes inevitably refer to numerical methods as well. To fully understand the relativistic geometrically thick accretion disc structure, we consider all three components of the fluid velocity to be non-zero. This implies that the magnetofluid can flow in all three directions surrounding the central black hole. As we get radially closer to the hole, the fluid flows faster in all those directions. However, as we move towards the equator along the meridional direction, the radial inflow becomes stronger from both the speed and the mass accretion rate points of view. Nonetheless, the vertical (meridional) speed and the rotation of the plasma disc become slower in that direction. Due to the presence of pressure gradient forces, a sub-Keplerian angular momentum distribution throughout the thick disc is expected as well. To get a concise analytical form of the rate of accretion, we assume that the radial dependency of radial and meridional fluid velocities is the same. This simplifying assumption leads to radial independency of mass accretion rate. The motion of the accreting plasma produces an azimuthal current whose strength is specified based on the strength of the external dipolar magnetic field. This current generates a poloidal magnetic field in the disc which is continuous across the disc boundary surface due to the presence of the finite resistivity for the plasma. The gas in the disc is vertically supported not only by the gas pressure but also by the magnetic pressure.