  It is thought that the spacetime geometry around black hole candidates is
described by the Kerr solution, but an observational confirmation is still
missing. Today, the continuum-fitting method and the analysis of the iron
K$\alpha$ line cannot unambiguously test the Kerr paradigm because of the
degeneracy among the parameters of the system, in the sense that it is
impossible with current X-ray data to distinguish a Kerr black hole from a
non-Kerr object with different values of the model parameters. In this paper,
we study the possibility of testing the Kerr nature of black hole candidates
with X-ray spectropolarimetric measurements. Within our simplified model that
does not include the effect of returning radiation, we find that it is
impossible to test the Kerr metric and the problem is still the strong
correlation between the spin and possible deviations from the Kerr geometry.
Moreover, the correlation is very similar to that of other two techniques,
which makes the combination of different measurements not very helpful.
Nevertheless, our results cannot be taken as conclusive and, in order to arrive
at a final answer, the effect of returning radiation should be properly taken
into account.
