Null geodesics in five-dimensional Reissner–Nordström anti-de Sitter black holes

Abstract

Abstract The study of the motion of photons around massive bodies is one of the most useful tools to find the geodesic structure associated with said gravitational source. In the present work, different possible paths projected in an invariant hyperplane are investigated, considering a five-dimensional Reissner–Nordström anti-de Sitter black hole. Also, we study some observational tests, such as the bending of light and the Shapiro time delay effect. Mainly, we found that the motion of photons follows the hippopede of a Proclus geodesic, which is a new type of trajectory of the second kind, the Limaçon of Pascal being their analog geodesic in four-dimensional Reissner–Nordström anti-de Sitter black hole.