Entropy correction and quasinormal modes of slowly rotating Kerr-Newman-de Sitter-like black hole in bumblebee gravity

Abstract: In this paper, we study the tunneling of fermion particle for slowly rotating Kerr-Newman-de Sitter-like (KNdS-like) black hole in bumblebee gravity model by applying the generalized uncertainty principle (GUP). The Hawking temperature of slowly rotating KNdS-like black hole has been modified under GUP. The quantum gravity effect reduces the rise of Hawking temperature of slowly rotating KNdS-like black hole. The modified Hawking temperature and the correction of black hole entropy are investigated by using the tunneling of fermion beyond the semiclassical approximation. We study the scalar field perturbation and effective potential of slowly rotating KNdS-like black hole in bumblebee gravity model by using Klein-G\"{o}rdon equation. The quasinormal modes for scalar perturbation is investigated using WKB approximation method and P{\"o}schl-Teller fitting method. The significant impact on the greybody factor, Hawking spectra and sparsity of Hawking radiation of the black hole are also studied in the presence of Lorentz violating parameter L.