MOTION AND TRAJECTORIES OF PARTICLES AROUND 3-DIMENSIONAL BLACK-HOLES

The motion of relativistic particles around three-dimensional black ho les following the Hamilton-Jacobi formalism is studied. It follows tha t the Hamilton-Jacobi equation can be separated and reduced by quadrat ures in analogy with the four-dimensional case. It is shown that (i) p articles are trapped by the black hole regardless of their energy and angular momentum; and (ii) matter always falls to the centre of the bl ack hole and cannot undertake motion with stable orbits as in four dim ensions. For the extreme values of the angular momentum of the black h ole, we were able to find exact solutions for the equations of motion and trajectories of a test particle.