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In ApJ (1974), Will solved the perturbation of a Schwarzschild black hole dueto a slowly rotating light concentric thin ring, using Green's functionsexpressed as infinite-sum expansions in multipoles and in the small mass androtational parameters. In a previous paper (ApJS 2017, Paper I), we expressedthe Green functions in closed form containing elliptic integrals, leaving justsummation over the mass expansion. Such a form is more practical for numericalevaluation, but mainly for generalizing the problem to extended sources wherethe Green functions have to be integrated over the source. We exemplified themethod by computing explicitly the first-order perturbation due to a slowlyrotating thin disc lying between two finite radii. After finding basicparameters of the system -- mass and angular momentum of the black hole and ofthe disc -- we now add further properties, namely those which reveal how thedisc gravity influences geometry of the black-hole horizon and those ofcircular equatorial geodesics (specifically, radii of the photon, marginallybound and marginally stable orbits). We also realize that, in the linear order,no ergosphere occurs and the central singularity remains point-like, and checkthe implications of natural physical requirements (energy conditions andsubluminal restriction on orbital speed) for the single-stream as well ascounter-rotating double-stream interpretations of the disc.

Schwarzschild black hole encircled by a rotating thin disc: Properties of perturbative solution