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

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