Perturbation of a Schwarzschild black hole due to a rotating thin disc

Abstract

Will (1974) treated the perturbation of a Schwarzschild black hole due to a slowly rotating light concentric thin ring by solving the perturbation equations in terms of a multipole expansion of the mass-and-rotation perturbation series. In the Schwarzschild background, his approach can be generalized to the perturbation by a thin disc (which is more relevant astrophysically), but, due to a rather bad convergence properties, the resulting expansions are not suitable for specific (numerical) computations. However, we show that Green's functions represented by the Will's result can be expressed in a closed form (without multipole expansion) which is more useful. In particular, they can be integrated out over the source (thin disc in our case), to yield well converging series both for the gravitational potential and for the dragging angular velocity. The procedure is demonstrated, in the first perturbation order, on the simplest case of a constant-density disc, including physical interpretation of the results in terms of a one-component perfect fluid or a two-component dust on circular orbits about the central black hole. Free parameters are chosen in such a way that the resulting black hole has zero angular momentum but non-zero angular velocity, being just carried along by the dragging effect of the disc.

24 pages, 4 figures, 2 tables

References in corpus (10)

• Free motion around black holes with discs or rings: between integrability and chaos - II
• NADA: A new code for studying self-gravitating tori around black holes
• Negative Komar Mass of Single Objects in Regular, Asymptotically Flat Spacetimes
• Self-gravitating ring of matter in orbit around a black hole: The innermost stable circular orbit
• Counterrotating perfect fluid discs as sources of electrovacuum static spacetimes
• Static axisymmetric rings in general relativity: How diverse they are
• Rotating systems, universal features in dragging and anti-dragging effects, and bounds onto angular momentum
• Dragging of inertial frames in the composed black-hole-ring system
• Gravitational field of a Schwarzschild black hole and a rotating mass ring
• Gravitomagnetic Field of Rotating Rings

Cited by in corpus (6)

• Extreme mass ratio inspirals into black holes surrounded by matter
• Gravitational Magnus effect
• Gravitomagnetism in the Lewis cylindrical metrics
• Schwarzschild black hole encircled by a rotating thin disc: Properties of perturbative solution
• Toward relativistic inspirals into black holes surrounded by matter
• Frame-dragging: meaning, myths, and misconceptions