QNMs of slowly rotating Einstein-Bumblebee Black Hole

TL;DR

This paper investigates how Lorentz-violating parameters affect the quasinormal modes of slowly rotating Einstein-bumblebee black holes, revealing significant impacts on the imaginary parts of QNM frequencies through numerical analysis.

Contribution

It provides a detailed analysis of QNMs in Einstein-bumblebee gravity, including master equations and numerical methods, highlighting the influence of Lorentz violation on black hole perturbations.

Findings

Lorentz-violating parameter significantly affects the imaginary part of QNM frequencies.

Higher accuracy in scalar QNMs up to second order in rotation.

Lorentz-violating effects on axial gravitational perturbations are similar to rotation effects.

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 $\ell$ is similar to that of increasing the rotation parameter $\tilde{a}$.