  We propose a new parametrization for testing the Kerr nature of astrophysical
black hole candidates. The common approaches focus on the attempt to constrain
possible deviations from the Kerr solution described by new terms in the
metric. Here we adopt a different perspective. The mass and the spin of a black
hole make the spacetime curved and we want to check whether they do it with the
strength predicted by general relativity. As an example, we apply our
parametrization to the black hole shadow, an observation that may be possible
in a not too distant future.
