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We present here the solution for accretion disk structure, which describes continuously the transition between optically thick and optically thin disk regions. We show that the disk structure equations without advection, used here, give two branches of solutions which do not intersect for L < L b < 0:6L Edd for = 1:0 and M BH = 10 8 M . For larger luminosities there are no global solutions of the equations without advection. We suggest, as one of the possibilities, that advection becomes important even before, at luminosities 0:1L Edd , when the inner disk regions become unstable due to radiation pressure dominance and induce the transition from optically thick to optically thin disk in the global solution.

Global solutions of optically thick advective accretion disks around black holes are constructed. The solutions are obtained by solving numerically a set of ordinary differential equations corresponding to a steady axisymmetric geometrically thin disk. We pay special attention to consistently satisfy the regularity conditions at singular points of the equations. For this reason we analytically expand a solution at the singular point, and use coefficients of the expansion in our iterative numerical procedure. We obtain consistent transonic solutions in a wide range of values of the viscosity parameter α and mass accretion rate. We compare two different form of viscosity: one takes the shear stress to be proportional to the pressure, while the other uses the angular velocity gradient-dependent stress.We find that there are two singular points in solutions corresponding to the pressureproportional shear stress. The inner singular point locates close to the last stable orbit around black hole. This point changes its type from a saddle to node depending on values of α and accretion rate. The outer singular point locates at larger radius and is always of a saddle-type. We argue that, contrary to the previous investigations, a nodal-type inner singular point does not introduce multiple solutions. Only one integral curve, which corresponds to the unique global solution, passes simultaneously the inner and outer singular points independently of the type of inner singular point. Solutions with the angular velocity gradient-dependent shear stress have one singular point which is always of a saddle-type and corresponds to the unique global solution. The structure of accretion disks corresponding to both viscosities are similar.

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Abstract.Gravity warps space and time into a funnel and generates a black hole when a cosmic body undergoes a catastrophic collapse. What can one say about the interior of a black hole? The important point is that inside a black hole the space radial direction becomes time, and time becomes a space direction. The path into the gravitational abyss of the interior of a black hole is a progression in time. There is a peculiar region inside a black hole where some characteristics of the space-time curvature become singular. We call this region singularity. The colossal tidal gravitational forces near singularity modify physical laws. Space and time are not only strongly curved near the singularity, but they split into quanta. The fall into the singularity is unstoppable for a body inside a black hole. This paper also addresses the following questions:Can one see what happens inside a black hole? Can a falling observer cross the singularity without being crushed? Can new baby universes arise inside a black hole? An answer to all these questions is probably "yes". We give also a brief review of the modern black hole astrophysics.