Perturbations of Einstein--Maxwell--phantom spacetime: Instabilities of charged Ellis--Bronnikov wormholes and quasinormal modes of black holes
Phantom scalar fields, as a viable candidate for dark energy, have been instrumental in eliminating spacetime singularities and constructing wormholes and regular black holes. We investigate the Einstein-Maxwell-phantom (EMP) framework, in which the Ellis-Bronnikov wormholes can be charged and regular black holes can be admitted. While the previous study has shown the stability of EMP wormholes under massless scalar field perturbations, we further perform a comprehensive linear analysis of the EMP spacetime through gravito-electromagnetic field perturbations in the axial sector and phantom scalar field perturbations under an approximate treatment in the polar sector. Our analyses of effective potentials and finite difference time profiles reveal the linear instability of EMP wormholes. In the black hole scenario, the quasinormal spectra of Type I black holes, where the matrix-valued direct integration method and the Prony method are used, recover those of general relativity (GR) when the scalar charge goes to zero. Finally, by introducing the concepts of generalized specific charge and mixing angle, we quantify how the relative contributions between the phantom scalar and the electromagnetic fields modify the quasinormal spectra, and we assess the prospects for detecting spectral deviations between the EMP theory and GR in gravitational wave observation.