QNMs of slowly rotating Einstein–Bumblebee black hole

Abstract

We have studied the quasinormal modes (QNMs) of a slowly rotating black hole with Lorentz-violating parameter in Einstein–Bumblebee gravity. We analyse the slow rotation approximation of the rotating black hole in the Einstein–Bumblebee gravity, and obtain the master equations for scalar perturbation, vector perturbation and axial gravitational perturbation, respectively. Using the matrix method and the continuous fraction method, we numerically calculate the QNM frequencies. In particular, for scalar field, it shows that the QNMs up to the second order of rotation parameter have higher accuracy. The numerical results show that, for both scalar and vector fields, the Lorentz-violating parameter has a significant effect on the imaginary part of the QNM frequencies, while having a relatively smaller impact on the real part of the QNM frequencies. But for axial gravitational perturbation, the effect of increasing the Lorentz-violating parameter $$\ell $$ ℓ is similar to that of increasing the rotation parameter $${\tilde{a}}$$ a ~ .

Probing the Lorentz Invariance Violation via Gravitational Lensing and Analytical Eigenmodes of Perturbed Slowly Rotating Bumblebee Black Holes

“…Overall, the condition of R ab = 0 determines whether the obtained spacetime is an exact solution of the vacuum Einstein-bumblebee action or not. Additional elaborations regarding this matter were presented in a very recent study by Liu et al [49].…”

“…When → 0, the metric reduces to the usual Kerr metric, while it becomes the static Einstein-bumblebee metric when a → 0. However, the metric given in Equation ( 10) is not a correct RBBH solution according to the findings of Maluf and Muniz [33]; their work was supported by [28,32,49].…”

“…Therefore, metric (17) can be viewed as the slow RBBH (SRBBH) estimation of the Einstein-bumblebee equation: Rab = 0. More information about this issue can be found in the Appendix section of Reference [49]. For the slowest or dilatory RBBH (DRBBH), one can consider the case of ã2 → 0 and hence r + → 2M and r − = r p → 0.…”

“…When we use expression (51) and the related metric functions, Equation (43) in Equation (49), and perform the small angle approximation, = tanψ 0 ≈ ψ 0 , the bending angle of the SRBBH can be found as follows:…”

“…The first RRBH solution was found in 2019 by Ding et al [25], who showed that the bumblebee field can impact the properties of rotating black holes, including their shapes, sizes, and gravitational attraction. This was followed by several other studies that investigated the effects of rotation on bumblebee black holes, including their QNMs, GFs, shadow, superradiant instability, and many other features [5,23,28,29,32,34,36,[44][45][46][47][48][49][50].…”