In this paper we give a detailed general relativistic formulation of the study of structure and stability of charged fluid disks around compact objects like black holes neglecting the self-gravitation of the disk itself. Having presented the general equations for equilibrium as well as for perturbations we solve explicitly the cases of rigidly and differentially rotating thin disks, with constant charge density and zero pressure, confined to the equatorial plane of the black hole. By using normal mode analysis we have analysed the stability of such disks under purely radial perturbations and find that the disks are generally stable.

In this paper we have presented a very general class of solutions for rotating fluid disks around massive objects (neglecting the self gravitation of the disk) with density as a function of the radial coordinate only and pressure being nonzero. Having considered a number of cases with different density and velocity distributions, we have analysed the stability of such disks under both radial and axisymmetric perturbations. For a perfect gas disk with γ= 5/3 the disk is stable with frequency (MG/r³)^1/2 for purely radial pulsation with expanding and contracting boundary. In the case of axisymmetric perturbation the critical γ_c for neutral stability is found to be much less than 4/3 indicating that such disks are mostly stable under such perturbations.

In this paper we have considered the structure of a thick perfect fluid disk of constant density rotating around a Schwarzschild black hole and its stability under axisymmetric perturbation. The inner edge of such disk cannot lie within 4m. The critical γ_c for neutral stability is found to be much less than 4/3 indicating that the disks are generally stable

Starting from a set of general equations governing the dynamics of a magneto-fluid around a compact object on curved space time, a fairly simple analytical solution for a test disc having only azimuthal component of velocity has been obtained. The electromagnetic field associated has a modified dipole configuration which admits a reasonable pressure profile for the case of fully relativistic treatment of Keplerian type of velocity distribution

We study the properties of the ’Newtonian forces’ acting on a test particle in the field of the Kerr black hole geometry. We show that the centrifugal force and the Coriolis force reverse signs at several different locations. We point out the possible relevance of such reversals particularly in the study of the stability properties of the compact rotating stars and the accretion discs in hydrostatic equilibria

In this paper we consider the equilibrium of a magnetofluid disc in Schwarzschild background with an external magnetic field, having the azimuthal and the radial components of the flow velocity nonzero. The electrical conductivityσ of the fluid is taken to be finite and thus the solution for the electromagnetic field is required to satisfy the Ohm’s law too with the four-current having onlyJ^ϕ andJ^t nonzero. The various physical parameters that have to correlate for possible equilibrium configurations are identified and their respective magnitudes estimated. It is found that for a given angular momentum distribution the inner edge of the disc can reach well within the usual6m limit only when the surface magnetic field of the central object is not too high when the matter density at the outer edge of the disc and the accretion rate are taken with reasonable limits

In this paper we discuss the equilibrium configuration of a plasma disc of infinite conductivity around a slowly rotating compact object, and obtain the pressure profiles, and the structure of magnetic field lines for co and counter-rotating discs.

In this paper, the analytical and numerical results of the stability analysis of the accretion disk at the inner boundary is presented. Including the effect of finite conductivity in the disk dynamics, a simple calculation considering only the radial perturbation has been carried out. Within local approximation, it is concluded that the disk is stable to Kelvin-Helmholtz and resistive electromagnetic modes whereas the magnetosonic mode can destabilise the disk structure.

A two-dimensional instability analysis for a magneto-keplerian disk flow around a compact object is presented here. Using the eigenvalue technique, linearly coupled perturbed equations have been numerically solved within the local approximation. It is concluded that Kelvin-Helmholtz, magnetosonic (fast and slow) and resistive electromagnetic modes exist. However, only the magnetosonic mode can destabilise the disk structure. Further, we discuss the properties of different modes as a function of disk parameters and plot the eigenmode structures for different physical quantities.