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Astrophysical black hole candidates are thought to be the Kerr black holepredicted by General Relativity. In order to confirm the Kerr-nature of theseobjects, we need to probe the geometry of the space-time around them and see ifthe observations are consistent with the predictions of the Kerr metric. Thatcan be achieved, for instance, by studying the properties of theelectromagnetic radiation emitted by the gas in the accretion disk. Thehigh-frequency quasi-periodic oscillations observed in the X-ray flux of somestellar-mass black hole candidates might do the job. As the frequencies ofthese oscillations depend only very weakly on the observed X-ray flux, it isthought they are mainly determined by the metric of the space-time. In thispaper, I consider the resonance models proposed by Abramowicz and Kluzniak andI extend previous results to the case of non-Kerr space-times. The emergingpicture is more complicated than the one around a Kerr black hole and there isa larger number of possible combinations between different modes. I thencompare the bounds inferred from the twin peak high-frequency quasi-periodicoscillations observed in three micro-quasars (GRO J1655-40, XTE J1550-564, andGRS 1915+105) with the measurements from the continuum-fitting method of thesame objects. For Kerr black holes, the two approaches do not provideconsistent results. In a non-Kerr geometry, this conflict may be solved if theobserved quasi-periodic oscillations are produced by the resonance $\nu_\theta: \nu_r = 3:1$, where $\nu_\theta$ and $\nu_r$ are the two epicyclicfrequencies. It is at least worth mentioning that the deformation from the Kerrsolution required by observations would be consistent with the one suggested inanother recent work discussing the possibility that steady jets are powered bythe spin of these compact objects.

journal of cosmology and astroparticle physics

Probing the space-time geometry around black hole candidates with the  resonance models for high-frequency QPOs and comparison with the  continuum-fitting method