EXACT GENERAL-RELATIVISTIC THIN DISKS AROUND BLACK-HOLES

The formalism for superposing two axially symmetric exact solutions of Einstein field equations, namely, a black hole and a thin disk, is pr esented. Three different families of disks are analyzed. The most impo rtant family gives the first known exact solution for a black hole sur rounded by a realistic heavy disk of matter. This family is the last t o be analyzed. The matter of the disks is made of counterrotating part icles with as many particles rotating to one side as to the other in s uch a way that the net angular momentum is zero and the disk is static . The first family consists of peculiar disks, in the sense that they are generated by two opposite dipoles. The particles of the disk have no pressure or centrifugal support. However, when there is a central b lack hole, centrifugal balance in the form of counterrotation appears. The second family is formed by disks of finite extent, the Morgan and Morgan disks. Within this family there ate three parameters to play w ith: the black hole and disk masses, and the disk radius. These two fa milies develop regions where matter moves with velocities greater than the velocity of light. The second family includes the remarkable conf iguration of a black hole surrounded by a disk made of tachyonic matte r up the edge, which is at the photonic orbit. In addition some config urations have regions where the energy density is negative in violatio n of the weak energy condition. This is the analogue of the strut that holds two particles apart in Weyl solutions, and which has a negative energy density. The last family admits configurations which do not co ntain tachyonic-regions and so has greater physical relevance. The dis ks of this family have an inner edge and a well-defined behavior at in finity. In the limit of a negligible disk mass one obtains the solutio n for an accretion (test-particle) disk.