Optical properties of regular black holes

We investigate the optical properties of regular black holes by interpreting static and spherically symmetric spacetimes as effective optical media. Starting from a geometrical definition of the refractive index, we compare the Schwarzschild optical behavior with four regular black hole geometries, namely the Bardeen, Hayward, Dymnikova and Fan-Wang solutions. We show that regularity at the core translates into a finite optical index, with quadratic corrections near the origin, in contrast with the singular Schwarzschild case. We then discuss how the gravitational version of Snell’s law can be used to characterize light bending in weak field and compact object regimes. Remarkably the deflection angle is studied for the same class of metrics. Physical interpretation on the so-obtained physics is thus explored.