Publikace ÚTF

Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk

Čížek, P. and Semerák, O.

Will, in 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 perturbation by a thin disk (which is
more relevant astrophysically), but, due to rather bad convergence properties, the resulting expansions are not
suitable for specific (numerical) computations. However, we show that Green’s functions, represented by Will’s
result, can be expressed in closed form (without multipole expansion), which is more useful. In particular, they can
be integrated out over the source (a thin disk in our case) to yield good 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 disk, including the physical interpretation of the results in terms of a onecomponent perfect fluid or a two-component dust in a circular orbit 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,
as it is just carried along by the dragging effect of the disk.
journal:The Astrophysical Journal Supplement Series

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