Horizon acoustics of the GHS black hole and the spectrum of AdS2

We uncover a novel structure in Einstein-Maxwell-dilaton gravity: an AdS2 × S2 solution in string frame, which can be obtained by a near-horizon limit of the extreme GHS black hole with dilaton coupling λ ≠ 1. Unlike the Bertotti-Robinson spacetime, our solution has independent length scales for the AdS2 and S2, with ratio controlled by λ. We solve the perturbation problem for this solution, finding the independently propagating towers of states in terms of superpositions of gravitons, photons, and dilatons and their associated effective potentials. These potentials describe modes obeying conformal quantum mechanics, with couplings that we compute, and can be recast as giving the spectrum of the effective masses of the modes. By dictating the conformal weights of boundary operators, this spectrum provides crucial data for any future construction of a holographic dual to these AdS2 × S2 configurations.