Quasinormal modes of scalar, electromagnetic, and gravitational perturbations in slowly rotating Kalb-Ramond black holes

TL;DR

This work studies how spontaneous Lorentz violation in Kalb-Ramond gravity affects black hole quasinormal modes in a slowly rotating, asymptotically flat background. By deriving master equations for scalar, electromagnetic, and axial gravitational perturbations to first order in the spin parameter, and solving the resulting eigenvalue problem with two independent numerical methods, the authors show that the Lorentz-violating parameter $\ell$ increases the real part and makes the imaginary part more negative of the QNM frequencies across sectors, with axial gravitational modes exhibiting the strongest sensitivity and a theoretical bound $\ell<0.5$. The combination of the continued-fraction method and matrix method provides robust, cross-validated QNM spectra, reinforcing the potential of gravitational-wave spectroscopy to probe Lorentz-violating signatures in KR gravity. These results highlight a concrete observational pathway to test beyond-GR physics via ringdown signals and motivate further work on higher-order rotation and fully coupled KR perturbations.

Abstract

We investigate quasinormal modes (QNMs) of scalar, electromagnetic, and axial gravitational perturbations in slowly rotating Kalb-Ramond (KR) black holes, where an antisymmetric tensor field induces spontaneous Lorentz symmetry breaking. Working consistently to first order in the dimensionless spin parameter, we derive the corresponding master equations and compute the QNM spectrum using both the continued-fraction and matrix methods, finding excellent agreement. Lorentz violation modifies the oscillation and damping rates in a unified manner across all perturbative sectors: the real part of the QNM frequency increases monotonically with the Lorentz-violating parameter $\ell$, while the imaginary part becomes more negative. Axial gravitational modes exhibit the strongest response, revealing an intrinsic theoretical bound $\ell< 0.5$, beyond which the spectrum approaches an extremal behavior. Our results highlight the potential of gravitational-wave spectroscopy to probe Lorentz-violating signatures in KR gravity.

Figures (4)

• Figure 1: Convergence of the CFM for the $l\!=\!m\!=\!2$ axial gravitational mode at $\tilde{a}\!=\!\ell\!=\!0.2$. The relative error $\delta_n$ decreases monotonically with the recurrence order $n$.
• Figure 2: The scalar frequencies in the $l=2, n=0$ mode are shown, where the upper and lower panels on the left correspond to the real and imaginary parts of the results, while the right panel presents the discrepancy between the matrix method and the CFM.
• Figure 3: The axial electromagnetic frequencies in the $l=2, n=0$ mode are shown, where the upper and lower panels on the left correspond to the real and imaginary parts of the results, while the right panel presents the discrepancy between the matrix method and the CFM.
• Figure 4: The axial gravitational frequencies in the $l=2, n=0$ mode are shown, where the upper and lower panels on the left correspond to the real and imaginary parts of the results, while the right panel presents the discrepancy between the matrix method and the CFM.