Exact solution of the photon equation in stationary Gödel-type and Gödel spacetimes

In this work, the photon equation (massless Duffin-Kemmer-Petiau equation) is written explicitly for the general type of stationary Gödel spacetimes and is solved exactly for the Gödel-type and the Gödel spacetimes. The harmonic oscillator behaviour of the solutions is discussed and the energy spectrum of the photon is obtained. Finally, the solution of Maxwell equations is found to show equivalence with the photon equation