Quasinormal Modes of a Coupled Scalar Field in the Acoustic Black Hole Spacetime

By using the third-order Wentzel--Kramers--Brillouin approximation and the monodromy methods, the quasinormal modes of a coupled scalar field in the canonical non-rotating acoustic black hole spacetime are investigated. It is shown that the coupling between the scalar field and background metric affects the quasinormal frequencies. At low overtones, both the real part and the magnitude of imaginary part increase with the couple factor ξ. For the larger ξ, both of them are almost linearly related to the couple factor. At high overtones, it is found that the frequency formula of the quasinormal modes is 2πω/k=ln1+2cos(√9-24ξ/5)π-i(2n+1)π, which means that when ξ is larger, the real part is the linear function of ξ^1/2.