Non-minimal Coupling Scalar Field Quasinormal Modes of Schwarzschild-de Sitter Black Hole with a Global Monopole

We use WKB approach and the finite difference method to research non-minimal coupling scalar field quasinormal modes of Schwarzschild-de Sitter black hole with a global monopole. The results show that the small positive constant η makes the scalar field decreasing, and the quasinormal modes of the real part increases but the imaginary parts decreases with the decreasing of the breaking scale ρ. While, when the horizon r _h increase, the actual oscillation frequency decreases, while the decay time scale increases. On the other hand, when the horizon r _h increases, the oscillation is difficult to stabilize.