Greybody factor and quasinormal modes of scalar and Dirac field perturbation in Schwarzschild-de Sitter-like black hole in Bumblebee gravity model

In this paper, we study the scalar and Dirac fields perturbation of Schwarzschild-de Sitter-like black hole in bumblebee gravity model. The effective potentials, greybody factors and quasinormal modes of the black hole are investigated by using the Klein–Gordon equation and Dirac equation. To compute the greybody factors for scalar and Dirac fields, we use the general method of rigorous bound. We also investigate the quasinormal mode using the third order WKB approximation method and Pöschl–Teller fitting method. The impact of Lorentz invariance violation parameter L and cosmological constant \(\varLambda \) to the effective potential, greybody factors and quasinormal modes are analyzed for different modes. Increasing the parameters \(\varLambda \) and L lower the effective potentials and consequently increases the rigorous bound on the greybody factors. Our findings show that the oscillation frequency and the damping rate decrease with increasing L. We analyze the Hawking temperature, power spectrum and sparsity of Hawking radiation. Both the peak of power spectrum and total power emitted decrease with increasing L. The effect of L on the shadow radius is also discussed.