Null geodesics in five-dimensional Reissner-Nordstr\"om anti-de Sitter black hole

TL;DR

This paper investigates photon trajectories around a five-dimensional Reissner-Nordström anti-de Sitter black hole, revealing new geodesic paths and analyzing observational effects like light bending and time delay.

Contribution

It introduces the hippopede of Proclus as a new photon geodesic in five-dimensional black holes and compares it with known four-dimensional analogues.

Findings

Photon motion follows the hippopede of Proclus geodesic.

Identifies the Limaçon of Pascal as a four-dimensional analogue.

Analyzes light bending and Shapiro delay effects.

Abstract

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