Alikram N. Aliev, Göksel Daylan Esmer, Pamir Talazan
The twin peaks high-frequency quasiperiodic oscillations (QPOs), which are observed in a number of black hole binaries, can be related to the epicyclic frequencies of the geodesic motion, thereby providing a testing ground for the spacetime geometry near the black holes. In this paper, we explore some observable effects of the geodesic motion in the spacetime of rotating black holes in general relativity and braneworld gravity. We focus on the description of the motion in terms of three fundamental frequencies: the orbital frequency, the radial and vertical epicyclic frequencies. For a Kerr black hole, we perform a detailed numerical analysis of these frequencies at the innermost stable circular orbits and beyond them as well as at the characteristic stable orbits, for which the radial epicyclic frequency attains its highest value. We find that the values of the radial and vertical epicyclic frequencies at particular orbits are in good qualitative agreement with the observed frequencies of the twin peaks QPOs in some black hole binaries. It is interesting that at the characteristic stable circular orbits, where the radial epicyclic frequency has maxima, the vertical and radial epicyclic frequencies exhibit an approximate 2 : 1 ratio even in the case of near-extreme rotation of the black hole. We also perform a similar analysis of the fundamental frequencies for a rotating braneworld black hole and argue that the existence of such a black hole with a negative tidal charge, whose angular momentum exceeds the Kerr bound in general relativity, does not confront with the observations of high frequency QPOs.
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http://arxiv.org/abs/1205.2838
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