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We review our contribution to infrared Renormalization Group (RG) effects to General Relativity in the context of galaxies. Considering the effective action approach to Quantum Field Theory in curved background, we argued that the proper RG energy scale, in the weak field limit, should be related to the Newtonian potential. In the galaxy context, even without dark matter, this led to a remarkably small gravitational coupling G variation (about or less than 10 −12 of its value per light-year), while also capable of generating galaxy rotation curves about as good as the best phenomenological dark matter profiles (considering both the rotation curve shape and the expected mass-to-light ratios). Here we also comment on related developments, open issues and perspectives.

The formalism for superposing two axially symmetric exact solutions of Einstein field equations, namely, a black hole and a thin disk, is presented. Three different families of disks are analyzed. The most important family gives the first known exact solution for a black hole surrounded by a realistic heavy disk of matter. This family is the last to be analyzed. The matter of the disks is made of counterrotating particles with as many particles rotating to one side as to the other in such 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 black 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 are three parameters to play with: the black hole and disk masses, and the disk radius. These two families develop regions where matter moves with velocities greater than the velocity of light. The second family includes the remarkable configuration of a black hole surrounded by a disk made of tachyonic matter up the edge, which is at the photonic orbit. In addition some configurations have regions where the energy density is negative in violation 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 contain tachyonic regions and so has greater physical relevance. The disks of this family have an inner edge and a well-defined behavior at infinity. In the limit of a negligible disk mass one obtains the solution for an accretion (test-particle) disk.PACS number(s): 04.20.Jb, 97.60.Lf