Nonradial perturbations of static charged wormholes

Abstract

We investigate the nonradial quasinormal-mode spectrum of static charged Ellis--Bronnikov wormholes in Einstein--Maxwell theory minimally coupled to a phantom scalar field. The background solutions are known in closed form and comprise three classes: subcritical, critical and supercritical, which all approach the extremal Reissner--Nordström geometry at the boundary of their domain of existence. We derive the linear perturbation equations for axial and polar sectors, including the coupled gravitational, electromagnetic and phantom-scalar degrees of freedom, and compute the corresponding spectra by means of a Chebyshev spectral method. The uncharged limit reproduces the known Ellis--Bronnikov spectrum and exhibits the expected electromagnetic isospectrality. For charged configurations we track the axial and polar branches across the three families of solutions and identify the effect of the charge on the damping times and oscillation frequencies. In particular, we find that charge can substantially reduce damping rates as the extremal Reissner--Nordström limit is approached. We also uncover a nonradial polar instability, most clearly visible in the fundamental $l=2$ branch for sufficiently large wormhole masses. This instability is distinct from the familiar radial Ellis--Bronnikov instability and shows that the nonradial sector imposes additional constraints on the dynamical viability of charged wormholes.