If astrophysical black hole candidates are the Kerr black holes predicted by General Relativity , the value of their spin parameter must be subject to the theoretical bound |a _ { * } | \leq 1 .
In this work , we consider the possibility that these objects are either non-Kerr black holes in an alternative theory of gravity or exotic compact objects in General Relativity .
We study the accretion process when their accretion disk is geometrically thick with a simple version of the Polish doughnut model .
The picture of the accretion process may be qualitatively different from the one around a Kerr black hole .
The inner edge of the disk may not have the typical cusp on the equatorial plane any more , but there may be two cusps , respectively above and below the equatorial plane .
We extend previous work on the evolution of the spin parameter and we estimate the maximum value of a _ { * } for the super-massive black hole candidates in galactic nuclei .
Since measurements of the mean radiative efficiency of AGNs require \eta > 0.15 , we infer the “ observational ” bound |a _ { * } | \lesssim 1.3 , which seems to be quite independent of the exact nature of these objects .
Such a bound is only slightly weaker than |a _ { * } | \lesssim 1.2 found in previous work for thin disks .