Propagation of light in the presence of gravity generated by static and spherically symmetric curved space-times using Maxwell equations

Abstract

In this manuscript, we present an alternative method for calculating null geodesics in General Static Isotropic Metrics in General Relativity and Extended Theories of Gravity. By applying a conformal transformation, we are able to consider an analogue gravity model, where curvature is encoded in the dielectric and magnetic properties of a medium. In other words, we pass from curved to flat space-times, where instead of the Einstein field equations, the Maxwell equations are solved. Within this geometrical background, the photon geodesics are calculated. Then, given different black hole and wormhole metrics, we apply this method obtaining an excellent agreement with respect to the exact solutions in the original gravity framework by committing angular deviations below $3^\circ$. Finally, we provide the image of a Schwarzschild black hole surrounded by a thin accretion disk, and the apparent image of a Morris & Thorne-like wormhole within an angular discrepancy below $4^\circ$.