Quasinormal modes of spherically symmetric black hole with cosmological constant and global monopole in bumblebee gravity

Abstract: This paper studies the scalar, electromagnetic field and Dirac field perturbations of spherically symmetric black hole within the framework of Einstein-bumblebee gravity model with global monopole and cosmological constant. We investigate the effective potentials, greybody factors and quasinormal modes (QNMs) by applying the Klein-Gordon equation, electromagnetic field equation and Dirac equation expressed in Newman-Penrose (NP) formalism. Using the general method of rigorous bound, the greybody factors of scalar, electromagnetic and Dirac field are derived. Applying the sixth order WKB approximation and Pad\'{e} approximation, the QNM frequencies are derived. We also discuss the impact of global monopole $\eta$, cosmological constant $\Lambda$ and Lorentz violation parameter $L$ to the effective potential, greybody factor and QNMs. Increasing the parameter $\eta$ prevents the rise of effective potential for both Schwarzschild-de Sitter (SdS)-like and Schwarzschild-Anti de Sitter (SAdS)-like black holes with global monopole and consequently increases the greybody factors. However, decreasing the parameter $L$ reduces the rise of effective potential for the SAdS-like black hole with global monopole and it increases the greybody factor but increasing the parameter $L$ has an opposite effect for SdS-like black hole with global monopole. It is also shown that the shadow radius increases with increasing the parameter $\eta$ for both dS and AdS cases. Increasing the value of $L$ tends to increase the shadow radius for dS black hole but it has an opposite effect in AdS case. A careful studying is being carried out to investigate how the absorption cross-section gets affected when the parameter $L$ appears into the picture.