Testing the Kerr black hole hypothesis
  It is thought that the final product of the gravitational collapse is a Kerr black hole and astronomers have discovered several good astrophysical candidates. While there is some indirect evidence suggesting that the latter have an event horizon, and therefore that they are black holes, a proof that the space-time around these objects is described by the Kerr geometry is still lacking. Recently, there has been an increasing interest in the possibility of testing the Kerr black hole hypothesis with present and future experiments. In this paper, I briefly review the state of the art of the field, focussing on some recent results and work in progress. 
Cosimo Bambi
gr-qc astro-ph.HE