Graviton-photon mixing. Exact solution in a constant magnetic field

In this work I study the effect of graviton-photon mixing in a constant external magnetic field and find for the first time in the literature exact solution of the equations of motion. In particular, I apply the effect of graviton-photon mixing to the case of interaction of gravitational waves with an external magnetic field and calculate the intensity Stokes parameter of the produced electromagnetic radiation. The obtained results are new and extend previous results obtained by using approximation methods.
Comment: 9 pages. A typo present in Eq. (19) which also propagated to Eq. (20) and Eq. (22) has been fixed. This typo was a missing $\omega^2$ in these equations