Quasinormal modes of an electrically charged Kalb-Ramond black hole

TL;DR

This work analyzes quasinormal modes of an electrically charged Kalb-Ramond black hole in a framework with spontaneous Lorentz violation. The odd-parity perturbations of the coupled gravitational and electromagnetic fields form a two-component, undecouplable system governed by a 2×2 matrix of effective potentials, requiring matrix-valued Leaver continued fractions and direct integration for the QNM spectrum. A discriminant-based eigenvalue recognition method is developed to identify mode types when decoupling is incomplete. The results show that the LV parameter $l=\xi_2 b^2/2$ shifts the real part of the fundamental QNMs approximately linearly while leaving the imaginary part largely unaffected, with a careful error analysis addressing boundary effects and expansion order; the RN and Schwarzschild limits validate the numerical approaches. Overall, the findings provide a principled approach to probing Planck-scale LV through black hole ringdown signals and offer practical guidance on parameter regimes and mode identification in undecouplable multi-field perturbations.

Abstract

Lorentz violation serves as a significant feature in many modified theories of gravity. In particular, spontaneous Lorentz violation induced by the Kalb-Ramond field has attracted considerable attention. Recently, an electrically charged black hole solution within the Kalb-Ramond framework was proposed. In this study, we investigate the quasinormal modes of the resulting ``undecouplable'' system using both the matrix-valued continued fraction method and the matrix-valued direct integration method. Additionally, we develop a new approach to distinguish between different modes in such ``undecouplable'' systems. An error analysis is performed, and the influence of Lorentz violation on the fundamental quasinormal modes is systematically analyzed within a suitable parameter range.

Figures (6)

• Figure 1: Error analysis.
• Figure 2: The trend of gravitational fundamental QNF with respect to violation parameter $l$ under different boundary cutoff $r_\mathrm{inf}$.
• Figure 3: Error analysis in RN cases under 3 order expansion at horizon and 5 order expansion at infinity.
• Figure 4: Effective potential components compared with RN case.
• Figure 5: Deviation of effective potential components from RN case at different violation parameter $l$.