Quasinormal Modes of Massive Scalar Perturbations in Slow-Rotation Bumblebee Black Holes with Traceless Conformal Electrodynamics

Abstract

We study electrically charged, slowly rotating black hole solutions in Einstein-Bumblebee gravity coupled to the traceless (conformal) ModMax nonlinear electrodynamics. By adopting a quadratic bumblebee potential that fixes the vacuum expectation value of the Lorentz-violating vector, we derive both the static configuration and its first-order rotating extension and demonstrate how the bumblebee parameter $\ell$ and the ModMax deformation $\gamma$ modify the horizon structure and the effective electric charge. We further investigate the dynamical properties of this spacetime by considering a massive scalar field perturbation. Using two independent numerical techniques, we compute the quasinormal mode (QNM) spectra and perform a comprehensive analysis of the influence of all relevant parameters, including the black hole spin, the Lorentz-violating coupling, the ModMax deformation, and the scalar field mass. Our results reveal coherent trends in the QNM frequencies, highlighting the interplay between Lorentz-symmetry breaking and nonlinear electrodynamics effects in black hole dynamics.

17 pages, 5 figures