Geodesic equations in the static and rotating dilaton black holes: Analytical solutions and applications

TL;DR

This paper analytically solves geodesic equations around static and rotating dilaton black holes using elliptic functions, classifies trajectories, and explores astrophysical implications.

Contribution

It provides explicit analytical solutions for geodesics in dilaton black holes and applies these to classify orbits and study astrophysical phenomena.

Findings

Analytical solutions for geodesics using Weierstrass elliptic functions

Classification of orbit types based on energy and angular momentum

Applications to astrophysical scenarios involving dilaton black holes

Abstract

In this paper, we consider the timelike and null geodesics around the static [GMGHS (Gibbons, Maeda, Garfinkle, Horowitz and Strominger), magnetically charged GMGHS, electrically charged GMGHS] and the rotating (Kerr-Sen dilaton-axion) dilaton black holes. The geodesic equations are solved in terms of Weierstrass elliptic functions. To classify the trajectories around the black holes, we use the analytical solution and effective potential techniques and then characterize the different types of the resulting orbits in terms of the conserved energy and angular momentum. Also, using the obtained results we study astrophysical applications.