Can we constrain the maximum value for the spin parameter of the super-massive objects in galactic nuclei without knowing their actual nature?

In 4-dimensional General Relativity, black holes are described by the Kerr solution and are subject to the bound vertical bar a(*)vertical bar <= 1, where a(*) is the black hole spin parameter. If current black hole candidates are not the black holes predicted in General Relativity, this bound does not hold and a(*) might exceed 1. In this Letter. I relax the Kerr black hole hypothesis and I find that the value of the spin parameter of the super-massive black hole candidates in galactic nuclei cannot be higher than about 1.2. A higher spin parameter would not be consistent with a radiative efficiency eta > 0.15. as observed at least for the most luminous AGN. While a rigorous proof is lacking, I conjecture that the bound vertical bar a(*)vertical bar less than or similar to 1.2 is independent of the exact nature of these objects. (C) 2011 Elsevier B.V. All rights reserved.