Testing the space-time geometry around black hole candidates with the analysis of the broad K$\alpha$ iron line. (arXiv:1211.2513v1 [gr-qc])

Testing the space-time geometry around black hole candidates with the analysis of the broad K$\alpha$ iron line. (arXiv:1211.2513v1 [gr-qc]):
Astrophysical black hole candidates are thought to be the Kerr black holes
predicted by General Relativity, but there is not yet a clear evidence that the
geometry of the space-time around these objects is really described by the Kerr
metric. In order to confirm the Kerr black hole hypothesis, we have to observe
strong gravity features and check they are in agreement with the ones predicted
by General Relativity. In this paper, I study what kind of information can be
extracted by analyzing the broad K$\alpha$ iron line, which is often seen in
the X-ray spectrum of both stellar-mass and super-massive black hole candidates
and whose shape is supposed to be strongly affected by the space-time geometry.
I extend previous studies in the literature. It turns out that there is a
strong degeneracy between the spin parameter and the deformation parameter;
that is, the line emitted around a Kerr black hole with a certain spin can be
very similar to the one coming from the space-time around a non-Kerr object
with a quite different spin. As in this paper I include the effect of the
disk's inclination angle, which is also a fit parameter, this degeneracy is
much stronger than the one found in previous studies. Despite that, the
analysis of the broad K$\alpha$ iron line is potentially more powerful than the
continuum-fitting method, as it can put a bound on possible deviations from the
Kerr geometry independently of the value of the spin parameter and without
additional measurements.