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

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.