Quasi-periodic oscillations around Kerr-MOG black holes

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Regular Article - Theoretical Physics

Quasi-periodic oscillations around Kerr-MOG black holes Martin Kološ1,a , Misbah Shahzadi2,b , Zdenˇek Stuchlík1,c 1

Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava, Bezruˇcovo nám.13, CZ-74601 Opava, Czech Republic 2 Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan

Received: 9 September 2019 / Accepted: 29 January 2020 / Published online: 17 February 2020 © The Author(s) 2020

Abstract The study of the quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole (BH) binaries can provide a powerful tool for testing the phenomena occurring in strong gravity regime. We thus present and apply to three known microquasars the model of epicyclic oscillations of Keplerian discs orbiting rotating BHs governed by the modified theory of gravity (MOG). We show that the standard geodesic models of QPOs can explain the observationally fixed data from the three microquasars, GRO 1655-40, XTE 1550-564, and GRS 1915+105. We perform a successful fitting of the high frequency (HF) QPOs observed in these microquasars, under assumption of MOG BHs, for epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models and discuss the corresponding constraints of parameters of the model, which are the mass and spin and parameter α of the BH.

1 Introduction The mysteries of the Universe have always been a source of great attractions for physicists. We are living in the Universe undergoing an accelerating expansion which is considered due to the presence of a mysterious form of repulsive gravity named as dark energy. The matter which can only be observed by its gravitational effects on the visible matter rather than seeing it directly is called dark matter (DM). Zwicky [54] deduced that there is an inconsistency between the luminous mass and the dynamical mass for the Coma cluster. He proposed that there must exist DM at the scale of clusters of galaxies. The observations of the rotation curves of spiral galaxies by Robin and Ford [33] also shows a e-mail:

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that the galaxies need missing mass in the context of Newtonian gravity. The main paradigm to explain the missing mass in the universe is the theory of DM, supposing that the unseen matter accounts for more than 20% of the Universe matter content. This hypothetical matter is made up of weakly interacting particles (i.e.,WIMPs) that may only interact with ordinary matter due to gravity. Experiments have been performed to directly detect DM particles by sensitive particle physics detectors, but no positive signal has been obtained until now [1]. An alternative approach to resolve the problem of DM is to modify the law of gravity. One of the first phenomenological efforts to modify the Newtonian gravity was Modified Newtonian Dyna