  On the basis of the Carter-Israel conjecture, today we believe that some
compact and massive objects in the Galaxy and in the Universe are Kerr black
holes. However, this idea cannot yet be confirmed by observations. We can
currently obtain reliable estimates of the masses of these objects, but we do
not know if the space-time around them is described by the Kerr metric and if
they have an event horizon. A fundamental limit for a Kerr black hole is the
Kerr bound $|a_*| \le 1$. Here I discuss some astrophysical implications
associated with the violation of this bound, which can thus be used to test the
Carter-Israel conjecture.
