Abstract
Nowadays we believe that a typical galaxy contains about 107 stellar-mass black holes and a single super-massive black hole at its center. According to general relativity, these objects are characterized solely by their mass M and by their spin parameter a*. A fundamental limit for a black hole in general relativity is the Kerr bound |a*| ⩽ 1, but the accretion process can spin it up to a* ≈ 0.998. If a compact object is not a black hole, the Kerr bound does not hold and in this letter I provide some evidences suggesting that the accretion process could spin the body up to a* > 1. While this fact should be negligible for stellar-mass objects, some of the super-massive objects at the center of galaxies may actually be super-spinning bodies exceeding the Kerr bound. Such a possibility can be tested by gravitational wave detectors like LISA or by sub-millimeter very long-baseline interferometry facilities.