Counterrotating Dust Disk Around a Schwarzschild Black Hole: New Fully Integrated Explicit Exact Solution

Abstract

The first fully integrated explicit exact solution of Einstein's field equations corresponding to the superposition of a counterrotating dust disk with a central black hole is presented. The obtained solution represents an infinite annular thin disk (a disk with an inner edge) around the Schwarsz-child black hole, and the corresponding to energy-momentum tensor agrees with all the energy conditions. The solution can also be interpreted as des-cribing a thin disk made of two counterrotating dust fluids that are also in agreement with all the energy conditions.

Keywords

• Classical General Relativity
• exact solutions
• self-gravitating systems
• Einstein equations