Superposition of Morgan and Morgan discs with a Schwarzschild black hole

The exact superposition of a black hole and a thin disc is considered. The disc is made of counter-rotating particles and belongs to the Morgan and Morgan family (1969). There are three parameters to play with, the black hole mass, and the disc mass and radius. The superposed exact solution comprehends several configurations, some yield mass ratios in conformity with the usual accretion discs. There is also a remarkable configuration of a black hole surrounded by a disc made of pure superluminal matter up to the edge, which is at the photonic orbit.