Quasinormal Modes and Dynamical Evolution of Scalar Fields in the Einstein-Bumblebee Theory with a Cosmological Constant

TL;DR

This study explores how Lorentz violation and a cosmological constant affect the quasinormal modes and evolution of scalar fields around black holes in Einstein-Bumblebee gravity, using both frequency and time domain analyses.

Contribution

It provides the first detailed analysis of scalar field QNMs in Einstein-Bumblebee gravity with a cosmological constant, highlighting the influence of Lorentz violation on black hole perturbations.

Findings

Increasing Lorentz violation parameter decreases QNM frequencies and damping rates.

Higher cosmological constant reduces the magnitude of QNM frequencies.

Time-domain results confirm the frequency-domain analysis of Lorentz violation effects.

Abstract

This paper investigates the dynamic behavior of static, spherically symmetric black holes within the Einstein-Bumblebee gravity model with a cosmological constant, focusing on scalar field perturbations. Through separation of the angular components, the scalar field perturbations outside the black hole are reduced to a purely radial main equation. The quasinormal modes (QNMs) of the system are then determined via the WKB approximation in the frequency domain, while the dynamic evolution of the system is examined in the time domain using finite difference methods. The eigenfrequencies of the waveforms from the time-domain evolution are fitted to cross-validate the frequency-domain results. The study finds that the Lorentz violation parameter $ \ell $ and the cosmological constant $ \Lambda $ significantly influence the QNMs. Specifically, as $ \ell $ increases, the real and imaginary components of the lower modes decrease, while in higher modes, the real part changes minimally, and the imaginary part decreases rapidly. An increase in $ \Lambda $ similarly results in a decrease in the overall QNM values. These results are supported by the time-domain analysis, providing a clearer picture of how Lorentz symmetry breaking affects the QNMs of de Sitter spacetime.