Metric and dilaton information from high-overtone quasinormal modes of analytic Einstein-Maxwell-dilaton black holes

Abstract

Black-hole interiors are hidden from exterior observers, yet their geometry can enter the high-overtone spectrum of linear perturbations. We study how this spectrum encodes metric and supporting-matter information in analytic Einstein--Maxwell--dilaton black holes. Coupling a neutral spectator to the dilaton at fixed UV dimension provides a matter-sensitive channel alongside the momentum response. For real-endpoint spacelike connections, the momentum response and mass-label dependence separate the metric exponents from the signed dilaton slope. Near the causal threshold, a complex endpoint controls the spectral family: the mass profiles approach a common value, producing a shared fractional correction, while regular propagation retains label dependence. This mechanism is present at criticality without an inner horizon and continues locally into timelike interiors. Exterior numerical spectra support the reconstruction and the leading complex-endpoint responses. Local scaling and probe coupling set the candidate responses, while wave connection determines their imprint on the exterior spectrum.