Late-time tail of a coupled scalar field in the background of a black hole with a global monopole

Using the technique of spectral decomposition, we investigated the late-time tails of massless and massive coupled scalar fields in the background of a black hole with a global monopole. We found that due to existence of the coupling between the scalar and gravitational fields, the massless scalar field decay faster at timelike infinity $i_{+}$, and so does the massive one in the intermediate late time. But the asymptotically late-time tail for the massive scalar field is not affected and its decay rate still is $t^{-5\mathrm{/}6}$.