  The relative acceleration between two nearby particles moving along
accelerated trajectories is studied, which generalizes the geodesic deviation
equation. The polarization content of the gravitational wave in Horndeski
theory is investigated by examining the relative acceleration between two
self-gravitating particles. It is found out that the longitudinal polarization
exists no matter whether the scalar field is massive or not. It would be still
very difficult to detect the enhanced longitudinal polarization with the
interferometer, as the violation of the strong equivalence principle of mirrors
used by interferometers is extremely small. However, the pulsar timing array is
promised to relatively easily detect the effect of the violation as neutron
stars have large self-energy. The advantage of using this method to test the
violation of the strong equivalence principle is that neutron stars are not
required to be present in the binary systems.
