Numerical coordinates are expanded in terms of Chebyshev polynomials. The system to be solved is obtained by writing Einstein’s equations in collocation space including regularity conditions on the axis and appropriate boundary conditions on both the horizon of the black hole and at spatial infinity. As in [9, 10], the system is solved iteratively, using the Newton–Raphson method.
Both the Newtonian and relativistic configurations are computed. The ratio between the mass of the black hole and the mass of the ring is varied from zero (no black hole) to 144. The inner mass shedding of the ring can be obtained. One of the most interesting results is the existence of configurations for which the ratio of the black hole angular momentum and the square of its mass exceeds one, contrary to what can be achieved for an isolated black hole.
Living Rev. Relativity 12, (2009), 1
This work is licensed under a Creative Commons License.