We examine a thick accretion disc in the presence of external gravity and intrinsic dipolar magnetic field due to a non-rotating central object. In this paper, we generalize the Newtonian theory of stationary axisymmetric resistive tori of Tripathy, Prasanna & Das (1990) by including the fully general relativistic features. If we are to obtain the steady state configuration, we have to take into account the finite resistivity for the magnetofluid in order to avoid the piling up of the field lines anywhere in the accretion discs. The efficient value of conductivity must be much smaller than the classical conductivity to be astrophysically interesting. The accreting plasma in the presence of an external dipole magnetic field gives rise to a current in the azimuthal direction. The azimuthal current produced due to the motion of the magnetofluid modifies the magnetic field structure inside the disc and generates a poloidal magnetic field for the disc. The solutions we have found show that the radial inflow, pressure and density distributions are strongly modified by the electrical conductivity both in relativistic and Newtonian regimes. However, the range of conductivity coefficient is different for both regimes, as well as that of the angular momentum parameter and the radius of the innermost stable circular orbit. Furthermore, it is shown that the azimuthal velocity of the disc which is not dependent on conductivity is sub-Keplerian in all radial distances for both regimes. Owing to the presence of pressure gradient and magnetic forces. This work may also be important for the general relativistic computational magnetohydrodynamics that suffers from the lack of exact analytic solutions that are needed to test computer codes.

The dynamics of an axisymmetric stationary disc of accreting magnetofluid with finite conductivity around a rotating compact object is presented here. Along with the Maxwell equations and the generalized Ohm law, the basic equations governing the motion of a finitely conducting plasma in a curved space–time around a slowly rotating compact object are derived. The finite electrical conductivity is taken into account for the plasma; however, the shear viscous stress is neglected, as well as the self‐gravity of the disc. In this case, energy dissipation occurs only through the finite resistivity. The magnetic stress takes the place of viscous stress in the standard disc model, and extracts angular momentum from the disc. The accreting plasma in the presence of an external dipole magnetic field gives rise to a current in the azimuthal direction. The azimuthal current produced as a result of the motion of the magnetofluid generates the magnetic field for the disc. Magnetic lines of force can penetrate the accretion disc because of the presence of finite resistivity. It has been shown that the dipolar magnetic field structure of the central black hole is modified inside the disc. In fact, the magnetic field lines are pushed outward and are continuous across the disc boundary. It has been demonstrated that the inward flow passing through a sub‐Alfvénic region becomes super‐Alfvénic to fall into the event horizon.

The dynamics of the stationary axisymmetric configuration of accreting magnetofluids surrounding a nonrotating compact object in the final stages of accretion flow is presented here. We discuss two classes of solutions for the angular momentum: a Keplerian solution, which demands no accretion flow for the fluids, and a non-Keplerian solution, which requires a radial inflow velocity for the matter. For the special case of no presence of electromagnetic fields, two sets of self-consistent analytical solutions of fully relativistic fluid equations are obtained separately for two different equations of state. The effect of the bulk viscosity coefficient on the physical functions was investigated for each state, as well as the bounds that exert on the free parameters due to last stages of the accretion-flow condition. To resolve the magnetohydrodynamical equations, we were inspired by previous sets of solutions, since the magnetofluid equations are just the same as the fluid ones in the case of vanishing electromagnetic fields. The azimuthal current in magnetofluids doesn't modify the dipolar configuration of the central object magnetic field, owing to the lack of a finite resistivity. The presence of this magnetic field doesn't affect the azimuthal velocity of the plasma, but does slow down its radial inflow, and decrease the density and pressure of the plasma. Despite the role importance of the bulk viscosity on the fluids' dynamics in the absence of electromagnetic fields, exerting the magnetic field decreases this role.

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.

Time evolution of a thick disc with finite conductivity around a nonrotating compact object is presented. Along with the Maxwell equations and the Ohm's law, the Newtonian limit of the relativistic fluid equations governing the motion of a finitely conducting plasma is derived. The magnetofluid is considered to possess only the poloidal components of the electromagnetic field. Moreover, the shear viscous stress is neglected, as well as the self-gravity of the disc. In order to solve the equations, we have used a self-similar solution. The main features of this solution are as follows. The azimuthal velocity is somewhat increased from the Keplerian value in the equator plane to the super-Keplerian values at the surface of disc. Moreover, the radial velocity is obtained proportional to the meridional velocity. Magnetofluid does not have any nonzero component of the current density. Subsequently, the electromagnetic force is vanished and does not play any role in the force balance. While the pressure gradient maintains the disc structure in latitudinal direction, magnetofluid has no accretion on the central compact object. Analogously to the parameter α in the standard model, our calculations contain one parameter η0 which specifies the size of the electrical resistivity.