  We analyze the gravitational perturbations induced by particles falling into
a three dimensional, asymptotically AdS black hole geometry. More specifically,
we solve the linearized perturbation equations obtained from the geodesic
motion of a ring-like distribution of test particles in the BTZ background.
This setup ensures that the U(1) symmetry of the background is preserved. The
non-asymptotic flatness of the background raises difficulties in attributing
the significance of energy and angular momentum to the conserved quantities of
the test particles. This issue is well known but, to the best of our knowledge,
has never been addressed in the literature. We confirm that the naive
expressions for energy and angular momentum are the correct definitions.
Finally, we put an asymptotically AdS version of the weak cosmic censorship to
a test: by attempting to overspin the BTZ black hole with test particles it is
found that the black hole cannot be spun-up past its extremal limit.
