Greybody factor for a rotating black hole with quintessential energy

This paper is devoted to deriving an analytic expression of the greybody factor for a rotating black hole surrounded by quintessence. Primarily, we transform the radial part of the Klein–Gordon equation into the standard Schrödinger equation through the tortoise coordinate to analyze the profile of the effective potential. Asymptotic solutions are obtained in two distinct regions, namely, the black hole and cosmological horizons determined by the quintessential field. We then extrapolate these solutions and match them smoothly in an intermediate region to extend the viability over the whole radial regime. To elaborate the significance of the analytical solution, we evaluate the emission rates and absorption cross-section for the massless scalar fields. It is found that the accelerated expansion of the universe corresponding to smaller values of the state parameter minimizes the effective potential and consequently increases the emission process of the scalar field particles.