Scalar particle in the Kiselev-anti-de-Sitter black hole background
In this work, we investigate the dynamics of a scalar particle in a black-hole spacetime surrounded by a cosmological constant and an anisotropic fluid. By solving the Klein--Gordon equation through a power series approach, we obtain quasibound states and the corresponding energy quasispectrum. We find that the quasispectrum can exhibit both real and imaginary components, depending on the model parameters, with the real component existing only under specific conditions. The numerical analysis shows that decreasing the cosmological constant and the anisotropic fluid parameter enhances the energy and increases the radiation in the region outside the event horizon, whereas stronger contributions from these surrounding fields tend to suppress the emitted radiation. We also analyze several asymptotic limits and recover the corresponding results for the Kiselev, de Sitter, and Schwarzschild black holes, providing consistency checks for our solutions. These results highlight the role of the surrounding matter distribution and cosmological contribution in modifying the dynamics and radiation of scalar fields in black hole spacetimes.