Quasinormal modes of a charged spherically symmetric black hole in bumblebee gravity

TL;DR

This paper analyzes quasinormal modes of a charged spherically symmetric black hole in bumblebee gravity, a Lorentz-violating extension of general relativity. It derives scalar and gravito-electromagnetic perturbation equations on the bumblebee background and computes QNMs using both continued fraction (CFM) and asymptotic iteration (AIM) methods, with special treatment for the coupled perturbations. The results show that increasing the Lorentz-violating parameter $l$ reduces damping (the imaginary parts of the frequencies) for all perturbations, while the real parts respond differently across perturbation types; the RN limit is recovered when $l=0$, validating the methods. The study demonstrates the reliability and complementary strengths of CFM and AIM in Lorentz-violating spacetimes and provides a quantitative baseline for how Lorentz violation impacts black hole ringdown signals.

Abstract

Recently, some of us have obtained exact charged spherically symmetric black hole solutions within the framework of bumblebee gravity, where the Lorentz symmetry is spontaneously broken due to the nonvanishing vacuum expectation value of the bumblebee field. In this work, we investigate the quasinormal modes of this black hole. We compute the quasinormal frequencies corresponding to the scalar perturbation and the gravito-electromagnetic coupled perturbation using both the continued fraction method and the asymptotic iteration method. A detailed comparison of the results obtained from the two approaches is presented to evaluate their accuracy and efficiency in this Lorentz-violating background.

Figures (5)

• Figure 1: The effective potential of the scalar field with $Q_0=0.2M$ and varying Lorentz-violating parameter $l$.
• Figure 2: The real parts (left) and imaginary parts (right) of the QNFs by using the CFM for the black hole with varying electric charge $Q_0$ and Lorentz-violating parameter $l$ (ranging from $0$ to $1$).
• Figure 4: The real parts (left) and imaginary parts (right) of the QNFs of the gravitational perturbation and the electromagnetic perturbation for the black hole with varying electric charge $Q_0$ (ranges from $0$ to $0.8M$) and Lorentz-violating parameter $l$ (ranges from $0$ to $1$), and the angular momentum $L=2$.
• Figure 5: The real parts (left) and imaginary parts (right) of the QNFs of the gravitational perturbation and the electromagnetic perturbation for the black hole with varying electric charge $Q_0$ (ranges from $0$ to $0.8M$) and Lorentz-violating parameter $l$ (ranges from $0$ to $1$), and the angular momentum $L=3$.
• Figure 6: The real parts (left) and imaginary parts (right) of the QNFs of the gravitational perturbation and the electromagnetic perturbation for the black hole with varying electric charge $Q_0$ (ranges from $0$ to $0.8M$) and Lorentz-violating parameter $l$ (ranges from $0$ to $1$), and the angular momentum $L=4$.