Real scalar field scattering with polynomial approximation around Schwarzschild–de Sitter black-hole

As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild–de Sitter black- hole. The complicated relationship between tortoise coordinate and radial coordinate is replaced by the approximate polynomial. The Schrdinger-like equation, the real boundary conditions and the polynomial approximation construct a full Sturm–Liouville type problem. Then this boundary value problem can be solved numerically for two limiting cases: the first one is the Nariai black-hole whose horizons are close to each other, the second one is the black-hole with the horizons widely separated. Compared with previous results (Brevik and Tian), the field near the event horizon and cosmological horizon can have a better description.