Geodesic Structure of the 2 + 1 Black Hole

TL;DR

This paper analyzes null and timelike geodesics around a 2+1 black hole, revealing differences between rotating and non-rotating cases, and discusses orbit bounds and spacetime transitions using Penrose diagrams.

Contribution

It provides a comprehensive analysis of geodesic structures in 2+1 black holes, including bounds and the effects of rotation, which was not fully explored before.

Findings

Complete geodesics exist only in rotating black holes.

Bounds for radial orbit sizes are established.

Possibility of spacetime transitions via Penrose diagrams is discussed.

Abstract

Null and timelike geodesics around a 2+1 black hole are determined. Complete geodesics of both types exist in the rotating black-hole background, but not in the spinless case. Upper and lower bounds for the radial size of the orbits are given in all cases and the possibility of passing from one black hole exterior spacetime to another is discussed using the Penrose diagrams. An analysis of particle motions by means of effective potentials and orbit graphs are also included.