Gravitational perturbation induced by a rotating ring around a Kerr
  black hole
  The linear perturbation of a Kerr black hole induced by a rotating massive
circular ring is discussed by using the formalism by Teukolsky, Chrzanowski,
Cohen and Kegeles. In these formalism, the perturbed Weyl scalars, $\psi_0$ and
$\psi_4$, are first obtained from the Teukolsky equation. The perturbed metric
is obtained in a radiation gauge via the Hertz potential. The computation can
be done in the same way as in our previous paper, in which we considered the
perturbation of a Schwarzschild black hole induced by a rotating ring. By
adding lower multipole modes such as mass and angular momentum perturbation
which are not computed by the Teukolsky equation, and by appropriately setting
the parameters which are related to the gauge freedom, we obtain the perturbed
gravitational field which is smooth except on the equatorial plane outside the
ring.
