Quasinormal Modes of a Massive Scalar Field in Slowly Rotating Einstein-Bumblebee Black Holes

TL;DR

This paper investigates how black hole spin, Lorentz-violating parameters, and scalar field mass affect quasinormal modes of slowly rotating Einstein-Bumblebee black holes, revealing sensitivities and spectral structure changes through numerical analysis.

Contribution

It introduces a detailed analysis of QNMs in Lorentz-violating rotating black holes using second-order slow-rotation expansion and numerical methods, highlighting new spectral features and sensitivities.

Findings

QNM frequencies are more sensitive to negative $\, ext{ell}$ variations.

Spectral 'cube' shows slight compression or expansion depending on parameters.

Richer structures and lifted degeneracy appear at second order.

Abstract

In this study, we examine the impacts of black hole spin, Lorentz-violating parameter, and the scalar field's mass on quasinormal modes (QNMs) of rotating Einstein-Bumblebee black holes, including computations up to the second-order expansion in rotation parameters. We investigate two classes of Lorentz-violating rotating black holes: one constructed via the Newman-Janis algorithm and the other obtained by solving the field equations through a series expansion. Within the slow-rotation approximation framework, we derive the master equations governing a massive scalar field and compute the corresponding QNM frequencies numerically using both the continued fraction method and the matrix method. The numerical results indicate that the QNM frequencies exhibit increased sensitivity to negative $\ell$ variations, which reduces the influence of the field mass parameter $\tilde{\mu}$. Meanwhile, the spectral "cube" of NJA black holes shows slight compression for $m>0$ with $ \ell>0 $ and expansion for $m<0$ with $ \ell>0 $ compared to another black holes, where $m$ is approximately proportional to the spin parameter at first order, while richer structures and lifted degeneracy emerge at second order.