Shear oscillations in the hadron-quark mixed phase

Inside neutron stars, the hadron-quark mixed phase is expected during the first order phase transition from the hadron phase to the quark phase. The geometrical structure of the mixed phase strongly depends on the surface tension at the hadron-quark interface. We evaluate the shear modulus which is one of the specific properties of the hadron-quark mixed phase. As an application, we study shear oscillations due to the hadron-quark mixed phase in neutron stars. We find that the frequencies of shear oscillations depend strongly on the surface tension; with a fixed stellar mass, the fundamental frequencies are almost proportional to the surface tension. Thus, one can estimate the value of surface tension via the observation of stellar oscillations with the help of the information on the stellar mass.