Schwarzschild black hole encircled by a rotating thin disc: Properties of perturbative solution
Kotlařík, P.; Semerák, O.; Čížek, P.
Will [Astrophys. J. 191, 521 (1974)] solved the perturbation of a Schwarzschild black hole due to a
slowly rotating light concentric thin ring, using Green’s functions expressed as infinite-sum expansions in
multipoles and in the small mass and rotational parameters. In a previous paper [P. Čížek and O. Semerák,
Astrophys. J. Suppl. Ser. 232, 14 (2017)], we expressed the Green functions in closed form containing
elliptic integrals, leaving just summation over the mass expansion. Such a form is more practical for
numerical evaluation, but mainly for generalizing the problem to extended sources where the Green
functions have to be integrated over the source. We exemplified the method by computing explicitly the
first-order perturbation due to a slowly rotating thin disc lying between two finite radii. After finding basic
parameters of the system—mass and angular momentum of the black hole and of the disc—we now add
further properties, namely those which reveal how the disc gravity influences geometry of the black-hole
horizon and those of circular equatorial geodesics (specifically, radii of the photon, marginally bound and
marginally stable orbits). We also realize that, in the linear order, no ergosphere occurs and the central
singularity remains pointlike, and check the implications of natural physical requirements (energy
conditions and subluminal restriction on orbital speed) for the single-stream as well as counter-rotating
double-stream interpretations of the disc.