PERTURBATIVE APPROACH TO THE INNER STRUCTURE OF A ROTATING BLACK-HOLE

This is the first in a series of papers analyzing the inner structure of a generic rotating black hole. The black hole is assumed to evolve from the gravitational collapse of an isolated rotating object in an e mpty asymptotically-flat universe. This paper covers the first stages of the evolution: from the gravitational collapse and the formation of a black hole, up to the stage where the black hole settles down to Ke rr. We shall discuss the generalization of Price's analysis (regarding the late-time asymptotic decay of perturbations outside the black hol e) from Schwarzschild to Kerr, and present preliminary results. We the n consider these external small perturbations as initial data for the evolution of perturbations inside the black hole. We demonstrate that an important region inside the black hole, which we call the late-time region (and which extends up to the inner horizon) experiences (arbit rarily) small initial perturbations. This, we argue, justifies the att empt to apply the small-perturbation approach to the black hole's inte rior. We discuss the physical significance of this late-time region. W e shall also outline the strategy we use for evolving the perturbation s from the event horizon to the inner horizon.