Black holes surrounded by thin rings and the stability of circular orbits

Abstract

The solution to the Einstein vacuum field equation associated with a nonlinear superposition of a Kerr black hole with a thin ring of constant density is studied. The method used is the vesture method of Belinsky and Zakharov. The Newtonian ring potential is approximated by a truncate multipolar expansion. This expansion is used as a seed solution in the above-mentioned method. Estimations of errors due to the truncation of the multipolar expansions are performed. The epicyclic and vertical stabilities of circular equatorial orbits related to particles moving around the system black hole surrounded by a ring are considered for both relativistic and Newtonian gravity. We find the unexpected effect of the duplication of the photon circular orbit for certain values of the parameters related to the black hole and ring.