A Simple Derivation of the Gertsenshtein Effect

As shown by Gertsenshtein in 1961, an external magnetic field can catalyze the mixing of graviton and photon states in a manner analogous to neutrino-flavor oscillations. We first present a straightforward derivation of the mechanism by a method based on unpublished notes of Freeman Dyson. We next extend his method to include boundary conditions and retrieve the results of Boccaletti et al. from 1970. We point out that, although the coupling between the graviton and photon states is extremely weak, the large magnetic fields around neutron stars $\sim 10^{14}$ G make the Gertsenshtein effect a plausible source of gravitons. We also point out that axion-photon mixing, a subject of active current research, is essentially the same process as the Gertsenshtein effect, and so the general mechanism may be of broad astrophysical and cosmological interest.