Stationary axially symmetric perturbations of a rotating black hole

A stationary axially symmetric perturbation of a rotating black hole due to a distribution of test matter is investigated. The Newman-Penrose spin coefficient formalism is used to derive a general set of equations describing the perturbed space-time. In a linear approximation we show that the mass and angular momentum of a rotating black hole is not affected by the perturbation. The metric perturbations near the horizon are given. We conclude that given a perturbing test fluid distribution, one can always find a corresponding metric perturbation such that the mass and angular momentum of the black hole are not changed. It was also noticed that when a M, those perturbed spin coefficients and components of the Weyl tensor which determine the intrinsic properties of the incoming null cone near the horizon grow indefinitely.Supported in part by the National Science Foundation under grant No. GP-36687X.On leave from the Institute of Theoretical Physics, University of Warsaw, Warsaw, Poland.