Timelike geodesics around a charged spherically symmetric dilaton black hole

TL;DR

This paper analyzes the trajectories of particles around charged dilaton black holes using effective potential methods, classifying orbit types without solving equations of motion, and visualizing them through numerical solutions.

Contribution

It introduces a qualitative classification of timelike geodesics around charged dilaton black holes based on effective potential analysis, distinguishing between extremal and non-extremal cases.

Findings

Effective potential varies between extremal and non-extremal black holes.

Orbit types can be classified without solving equations of motion.

Numerical solutions visualize particle trajectories.

Abstract

In this paper we study the timelike geodesics around a spherically symmetric charged dilaton black hole. The trajectories around the black hole are classified using the effective potential of a free test particle. This qualitative approach enables us to determine the type of the orbit described by the test particle without solving the equations of motion, if the parameters of the black hole and the particle are known. The connections between these parameters and the type of orbit described by the particle are obtained. To visualize the orbits we solve numerically the equation of motions for different values of the parameters envolved in our analysis. The effective potential of a free test particle looks different for a non-extremal and an extremal black hole, therefore we have examined separately these two types of black holes.