X-ray spectropolarimetric measurements of the Kerr metric

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.