Equipotential Photon Surfaces are timelike and totally geodesic hypersurfaces in a static spacetime, such that the lapse function and the electric potential are constant at each time on their connected components. They are very interesting objects from the physical point of view and they have mathematical properties that allow us to analyse them adapting techniques developed for the study of Black Hole Horizons.
As a result of a project with Borghini and Cederbaum, I will discuss static electrovacuum spacetimes in presence of a connected Horizon or a connected Equipotential Photon Surface, providing a characterization of the Reissner-Nordström spacetime.
For this purpose, an approach via potential theory developed by Agostiniani and Mazzieri will be adopted, allowing not to assume the regular foliation of the spacetime by the lapse function, necessary for many other methods. This strategy yields a clear characterization of the spatial slices of the equipotential photon surfaces in sub-extremal, extremal and super-extremal Reissner-Nordström.