Astrophysical black hole candidates are thought to be the Kerr black hole predicted by General Relativity. However, in order to confirm the Kerr-nature of these objects, we need to probe the geometry of the space-time around them and check that observations are consistent with the predictions of the Kerr metric. That can be achieved, for instance, by studying the properties of the electromagnetic radiation emitted by the gas in the accretion disk. The high-frequency quasi-periodic oscillations observed in the X-ray flux of some stellar-mass black hole candidates might do the job. As the frequencies of these oscillations depend only very weakly on the observed X-ray flux, it is thought they are mainly determined by the metric of the space-time. In this paper, I consider the resonance models proposed by Abramowicz and Kluzniak and I extend previous results to the case of non-Kerr space-times. The emerging picture is more complicated than the one around a Kerr black hole and there is a larger number of possible combinations between different modes. I then compare the bounds inferred from the twin peak high-frequency quasi-periodic oscillations observed in three micro-quasars (GRO J1655-40, XTE J1550-564, and GRS 1915+105) with the measurements from the continuum-fitting method of the same objects. For Kerr black holes, the two approaches do not provide consistent results. In a non-Kerr geometry, this conflict may be solved if the observed quasi-periodic oscillations are produced by the resonance ν θ : ν r = 3 : 1, where ν θ and ν r are the two epicyclic frequencies. It is at least worth mentioning that the deformation from the Kerr solution required by observations would be consistent with the one suggested in another recent work discussing the possibility that steady jets are powered by the spin of these compact objects.
At sufficiently low temperatures localized defects or impurities change into excitations that move practically freely through a crystal. As a result instead of the ordinary diffusion of defects, there arises a flow of a liquid consisting of "defectons" and "impuritons." It is shown that at absolute zero in crystals with a large amplitude of the zero-point oscillations (for example, in crystals of the solid helium type) zero-point defectons may exist, as a result of which the number of sites of an ideal crystal lattice may not coincide with the number of atoms. The thermodynamic and acoustic properties of crystals containing zero-point defectons are discussed. Such a crystal is neither a solid nor a liquid. Two kinds of motion are possible in it; one possesses the properties of motion in an elastic solid, the second possesses the properties of motion in a liquid. Under certain conditions the "liquid" type of crystal motion possesses the property of superfluidity. Similar effects should also be observed in quasiequilibrium states containing a given number of defectons.
Supersolidity of glasses is explained as a property of an unusual state of condensed matter. This state is essentially different from both normal and superfluid solid states. The mechanism of the phenomenon is the transfer of mass by tunneling two level systems.
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