In 4-dimensional General Relativity , black holes are described by the Kerr solution and are subject to the bound |a _ { * } | \leq 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 can not 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 |a _ { * } | \lesssim 1.2 is independent of the exact nature of these objects .