Abstract
By using the Pöschl–Teller potential approximation, the quasinormal modes of the Reissner–Nordström de Sitter black hole for the axial and polar gravitational perturbations are investigated. It is shown that the magnitude of imaginary part decreases as the cosmological constant increases, but it increases as the charge, or the overtone number or the orbital angular momentum increases. The imaginary part is almost linearly related to the real part as cosmological constant changes for a fixed charge. It is also found that the gravitational quasinormal modes are the same for both the axial and polar perturbations, which proves that the quasinormal modes are determined only by the parameters of the black hole and are independent of the initial perturbations.