Timelike geodesics for five-dimensional Schwarzschild and Reissner-Nordstr\"om Anti-de Sitter black holes

TL;DR

This paper analyzes the motion of particles around five-dimensional Schwarzschild and Reissner-Nordström Anti-de Sitter black holes, providing detailed descriptions of trajectories using elliptic functions.

Contribution

It offers a detailed analysis of timelike geodesics in higher-dimensional black holes, including explicit solutions for particle trajectories.

Findings

Multiple types of particle orbits identified

Explicit solutions for trajectories using elliptic functions

Enhanced understanding of particle dynamics in higher-dimensional spacetimes

Abstract

The timelike structure of the five-dimensional Schwarzschild and Reissner-Nordstr\"om Anti-de Sitter black holes is studied in detail. Different kinds of motion are allowed and studied by using an adequate effective potential. Then, by solving the corresponding equations of motion, several trajectories and orbits are described in terms of Weierstrass elliptic functions and elementary functions for neutral particles.