Near-Ad S2 perturbations and the connection with near-extreme Reissner-Nordstrom

The geometry very near the horizon of a near-extreme Reissner-Nordstrom black hole is described by the direct product of a near-Ad S-2 spacetime with a two-sphere. While near-Ad S-2 is locally diffeomorphic to Ad S-2 the two connect differently with the asymptotically flat part of the geometry of (near-)extreme Reissner-Nordstrom. In previous work, we solved analytically the coupled gravitational and electromagnetic perturbation equations of AdS(2)xS(2) and the associated connection problem with extreme Reissner-Nordstrom. In this paper, we give the solution for perturbations of near-AdS(2) x S-2 and make the connection with near-extreme Reissner-Nordstrom. Our results here may also be thought of as computing the classical scattering matrix for gravitational and electromagnetic waves which probe the region very near the horizon of a highly charged spherically symmetric black hole.