In general , it is very difficult to test the Kerr-nature of an astrophysical black hole candidate , because it is not possible to have independent measurements of both the spin parameter a _ { * } and possible deviations from the Kerr solution .
Non-Kerr objects may indeed look like Kerr black holes with different spin .
However , it is much more difficult to mimic an extremal Kerr black hole .
The black hole candidate in Cygnus X-1 has the features of a near extremal Kerr black hole , and it is therefore a good object to test the Kerr black hole paradigm .
The 3 \sigma -bounds a _ { * } > 0.95 and a _ { * } > 0.983 reported in the literature and valid in the Kerr spacetime become , respectively , a _ { * } > 0.78 and |g / M| < 0.41 , and a _ { * } > 0.89 and |g / M| < 0.28 in the Bardeen metric , where g is the Bardeen charge of the black hole .