Strong lensing and Hawking spectra of charged black hole under Lorentz violation theory

In this paper, we investigate the strong gravitational lensing effects around the Reissner-Nordstr{ö}m-like black hole (RN-like BH) in bumblebee gravity. We calculate the lensing quantities such as deflection angle, radius of the photon sphere, angular separation, relativistic image characteristics, Einstein ring and time delay. By taking the supermassive black holes (SMBHs) like Sgr A*, M87*, NGC 1332, NGC 4649 etc. as RN-like BH, we compute the lensing observables and compare with the observables associated with the Reissner-Nordström black hole (RNBH). The quasinormal modes (QNMs) of massless Dirac field perturbation of Reissner-Nordstr{ö}m-de Sitter-like (RNdS-like) BH are also calculated. We discuss the behaviour of both real and imaginary parts of QNM frequencies with varying of $Q$ and $L$. It shows the damping rate and the oscillation frequency decrease with increasing $L$ but it has the opposite effect for the increase of $Q$. We further explore the detectability of QNMs by LIGO and LISA, and study the impact of $L$ and $Q$ on the detectable BH mass range. Further, we investigate the behaviour of greybody factor (GF) of RNdS-like BH in bumblebee gravity and find that the probability of wave transmission increases with increasing $L$ but decreases with the increase of $Q$. The behaviour of absorption cross section and sparsity of Hawking radiation for different values of $L$ and $Q$ are also analysed graphically.