A study of geodesic motion in a (2+1)-dimensional charged BTZ black hole

TL;DR

This paper derives and solves the equations of geodesic motion around a (2+1)-dimensional charged BTZ black hole, revealing particle trajectories using advanced elliptic functions and potential analysis.

Contribution

It provides explicit solutions for geodesics of both massive and massless particles in a charged BTZ black hole spacetime, using elliptic functions and effective potential methods.

Findings

Explicit geodesic solutions for massive particles

Explicit geodesic solutions for massless particles

Trajectories characterized by energy and angular momentum

Abstract

This study is purposed to derive the equation of motion for geodesics in vicinity of spacetime of a (2 + 1)-dimensional charged BTZ black hole. In this paper, we solve geodesics for both massive and massless particles in terms of Weierstrass elliptic and Kleinian sigma hyper-elliptic functions. Then we determine different trajectories of motion for particles in terms of conserved energy and angular momentum and also using effective potential.