Horizon Acoustics of the GHS Black Hole and the Spectrum of ${\rm AdS}_2$

TL;DR

This paper discovers a new ${ m AdS}_2 imes S^2$ solution in Einstein-Maxwell-dilaton gravity, analyzes its perturbations, and computes the spectrum of modes, providing essential data for potential holographic duals.

Contribution

It introduces a novel ${ m AdS}_2 imes S^2$ solution with independent scales and analyzes its perturbations, advancing understanding of holographic duals for such geometries.

Findings

New ${ m AdS}_2 imes S^2$ solution with independent length scales

Explicit spectrum of propagating modes and their effective potentials

Computed conformal weights for boundary operators

Abstract

We uncover a novel structure in Einstein-Maxwell-dilaton gravity: an ${\rm AdS}_2 \times S^2$ solution in string frame, which can be obtained by a near-horizon limit of the extreme GHS black hole with dilaton coupling $\lambda \neq 1$. Unlike the Bertotti-Robinson spacetime, our solution has independent length scales for the ${\rm AdS}_2$ and $S^2$, with ratio controlled by $\lambda$. 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 ${\rm AdS}_2\times S^2$ configurations.