Scalar field scattering by a Lifshitz black hole under a nonminimal coupling

We study the behavior of a scalar field under a z=3 Lifshitz black hole background, in a way which is nonminimally coupled to the gravitational field. A general analytical solution is obtained along with two sets of quasinormal modes associated to different boundary conditions which can be imposed on the scalar field; a nonminimal coupling parameter appears explicitly on these solutions. Stability of quasinormal modes can be studied and ensured for both cases. Also, the reflection and absorption coefficients are calculated, as well as the absorption cross section which features an interesting behavior because of being attenuated by terms strongly dependant on the nonminimal coupling. By a suitable change of variables, a soliton solution can also be obtained, and the stability of the quasinormal modes are studied and ensured.