The interaction between a rotating, spherical shell of matter and a central black hole

Astronomy and Astrophysics – Astronomy

Scientific paper

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Black Holes (Astronomy), Electromagnetic Fields, Gravitational Effects, Rotating Matter, Spherical Shells, Angular Momentum, Angular Velocity, Horizon, Mass Distribution, Multipoles, Perturbation Theory

Scientific paper

An investigation is conducted of the behavior of a black hole when placed at the center of a rotating, spherical shell of matter. The distribution of matter on the shell is constrained only to be axisymmetric about the rotation axis of the shell (which is distinct from the rotation axis of the hole), and to represent a small perturbation to the background geometry, as determined by the Kerr metric of the black hole. The perturbed metric due to the shell, at its center, in the absence of the black hole, is also calculated, and from it the 'electric' and 'magnetic' components of the corresponding Weyl tensor. It is seen that the spin-down law for the hole may be expressed in terms of these components, and when so expressed bears a resemblance to the spin-down law describing the perturbation by a uniform electric or magnetic field.

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