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Equilibrium configurations of self-gravitating magnetized toroid–central compact object systems have been constructed in the framework of the Newtonian gravity. We have succeeded in including not only poloidal but also toroidal magnetic fields under the ideal magnetohydrodynamic approximation. We find two new and interesting results about the critical equilibrium states of such systems beyond which no equilibrium states are allowed to exist. First, there appear critical distances from the central compact objects to the inner surfaces of the magnetized toroids. Furthermore, these critical distances are much larger than the distances of the innermost stable circular orbits. It implies that even if these systems would be treated in the framework of general relativity, there would appear cusp structures of the effective total potential of the gravitational and magnetic forces for strongly magnetized toroids which are different from the general relativistic cusp structures. Secondly, since the strength of the magnetic field for the critical equilibrium configurations is roughly if the mass of the central object is and the maximum density of the toroid is , the existence of equilibrium states of toroids around compact objects seems to set limit to the maximum value of the magnetic field of the system to be , i.e. no stronger magnetic fields can be realized for the systems consisting of magnetized toroids and central compact objects with the masses around the typical neutron star mass. The value of the maximum density of the toroid, , is taken from the theoretical computational results of binary neutron star merging simulations in full general relativity. [ABSTRACT FROM AUTHOR]

Equations of fully general relativistic radiation hydrodynamics around a rotating black hole are derived by using the Kerr–Schild coordinate where there is no coordinate singularity at the event horizon. Since the radiation interacts with matter moving with relativistic velocities near the event horizon, the interplay between the radiation and the matter should be described fully relativistically. In the formalism used in this study, while the interactions between matter and radiation are introduced in the comoving frame, the equations and the derivatives for the description of the global evolution of both the matter and the radiation are given in the Kerr–Schild frame which is a frame fixed to the coordinate describing the central black hole. As a frame fixed to the coordinate, we use the locally non-rotating reference frame representing a radially falling frame when the Kerr–Schild coordinate is used. Around the rotating black hole, both the matter and the radiation are affected by the frame-dragging effects. [ABSTRACT FROM AUTHOR]

Equations of fully general relativistic radiation hydrodynamics in Kerr space–time are derived. While the interactions between matter and radiation are introduced in the comoving frame, the derivatives used when describing the global evolutions of both the matter and the radiation are given in the Boyer–Lindquist frame (BLF) which is a frame fixed to the coordinate describing the central black hole. Around a rotating black hole, both the matter and the radiation are influenced by the frame-dragging effects due to the black hole's rotation. As a fixed frame, we use the locally non-rotating reference frame (LNRF) which is one of the orthonormal frame. While the special relativistic effects such as beaming effects are introduced by the Lorentz transformation connecting the comoving frame and the LNRF, the general relativistic effects such as frame dragging and gravitational redshift are introduced by the tetrads connecting the LNRF and the BLF. [ABSTRACT FROM AUTHOR]

The stationary hydrodynamic equations for the transonic accretion discs and flows around rotating black holes are presented by using the Kerr–Schild coordinate where there is no coordinate singularity at the event horizon. We use two types of the causal viscosity prescription, and the boundary conditions for the transonic accretion flows are given at the sonic point. For one type of the causal viscosity prescription we also add the boundary conditions at the viscous point where the accreting radial velocity is nearly equal to the viscous diffusion velocity. Based on the formalism for the transonic accretion discs, after we present the calculation method of the transonic solutions, the horizon-penetrating transonic solutions which smoothly pass the event horizon are calculated for several types of the accretion flow models: the ideal isothermal flows, the ideal and the viscous polytropic flows, the advection-dominated accretion flows with the relativistic equation of state, the adiabatic accretion discs, the standard accretion discs, the supercritical accretion discs. These solutions are obtained for both non-rotating and rotating black holes. The calculated accretion flows plunge into black hole with finite three-velocity smaller than the speed of light even at the event horizon or inside the horizon, and the angular velocities of the accretion flow at the horizon are generally different from the angular velocity of the frame dragging due to the black hole's rotation. These features contrast to the results obtained by using the Boyer–Lindquist coordinate with the coordinate singularity at the horizon. [ABSTRACT FROM AUTHOR]