Null geodesics in the Reissner-Nordstr\"om Anti-de Sitter black holes

TL;DR

This paper analyzes null geodesics in Reissner-Nordström Anti-de Sitter black holes, providing exact elliptic function solutions and classifying photon orbits based on charge, mass, and cosmological constant.

Contribution

It offers the first exact elliptic function solutions for photon trajectories in these black holes and classifies orbits using impact parameters.

Findings

Exact elliptic solutions for null geodesics

Classification of photon orbits by impact parameter

Detailed dependence of trajectories on charge, mass, and cosmological constant

Abstract

In this work we address the study of null geodesics in the background of Reissner-Nordstr\"om Anti de Sitter black holes. We compute the exact trajectories in terms of elliptic functions of Weierstrass, obtaining a detailed description of the orbits in terms of charge, mass and the cosmological constant. The trajectories of the photon are classified using the impact parameter.