Geodesic Structure of the 2 + 1 Black Hole
  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. 
Norman Cruz, Cristi\'an Mart\'inez and Leda Pe\~na