Quansinormal modes of static and spherically symmetric black holes with the derivative coupling

We investigate the quasinormal modes of a class of static and spherically symmetric black holes with the derivative coupling. The derivative coupling has rarely been paid attention to the study of black hole quasinormal modes. Specifically, we study the effect of derivative coupling on the quasinormal modes for four kinds of black holes. They are Reissner-Nordstrom black holes, Bardeen black holes, noncommunicative geometry inspired black holes and dilaton black holes. These black holes are not the solutions of vacuum Einstein equations which guarantees the effect of derivative coupling is not trivial. We find the influence of derivative coupling on the quasinormal modes roughly mimics the overtone numbers. In other words, there is a qualitative similarity in the trend of quasinormal modes frequencies due to increasing either the coupling constant and the overtone number.