Perturbations of Einstein--Maxwell--phantom spacetime: Instabilities of charged Ellis--Bronnikov wormholes and quasinormal modes of black holes

TL;DR

The paper develops a linear perturbation analysis of Einstein–Maxwell–phantom spacetimes, focusing on axial gravito‑electromagnetic perturbations and an approximate polar phantom‑scalar sector. It demonstrates linear instability for EMP wormholes due to phantom coupling, while Type I EMP black holes remain perturbatively stable and reproduce RN behavior as the scalar charge vanishes. By introducing a generalized specific charge and a mixing angle, the authors quantify how phantom and electromagnetic fields reshape quasinormal spectra and assess the prospects for detecting such deviations with gravitational‑wave observations. The results establish a clear dichotomy between wormhole and black‑hole configurations in EMP theory and outline observational paths for testing phantom hair in the strong‑field regime.

Abstract

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.

Figures (6)

• Figure 1: The effect of the azimuthal number $l$ of EMP wormholes on the effective potential and the time profile of the phantom scalar field perturbation with $q=1.6$, $Q=1$, $\gamma_1=-10$ and $\gamma_2=2$.
• Figure 2: The effect of the scalar charge $q$ of Type I black holes on the QNFs with $\gamma_1=1/4$, $\gamma_2=2q$, $Q_\mathrm{e}/M=2/5$ and $l=2$.
• Figure 3: The effect of the mixing angle $\vartheta$ of Type I black holes on the fundamental QNFs of the phantom scalar field perturbation with $l=2$.
• Figure 4: The effect of the mixing angle $\vartheta$ of Type I black holes on the fundamental QNFs of the electromagnetic field perturbation with $l=2$.
• Figure 5: The effect of the mixing angle $\vartheta$ of Type I black holes on the fundamental QNFs of the gravitational field perturbation with $l=2$.