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 |a⁎|⩽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 η>0.15, as observed at least for the most luminous AGN. While a rigorous proof is lacking, I conjecture that the bound |a⁎|≲1.2 is independent of the exact nature of these objects.