Interaction of plane gravitational waves with a Fabry-Perot cavity in the local Lorentz frame

We analyze the interaction of plane '+'-polarized gravitational waves with a Fabry-Perot cavity in the local Lorentz frame of the cavity input mirror outside of the range of long-wave approximation with the force of radiation pressure taken into account. The obtained detector response signal is represented as a sum of two parts: (i) the phase shift due to displacement of the movable mirror under the influence of gravitational wave and the force of light pressure, and (ii) the phase shift due to direct interaction of gravitational wave with light wave inside the cavity. We obtain formula for the movable mirror law of motion paying close attention to the phenomena of optical rigidity, radiative friction and direct coupling of gravitational wave to light wave. Some issues concerning the detection of high-frequency gravitational waves and the role of optical rigidity in it are discussed. We also examine in detail special cases of optical resonance and small detuning from it and compare our results with the known ones.