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We study the motion of test particles around the Kerr─Bertotti─Robinson (KBR) black hole (BH) and explore how the three defining parameters, the mass M, rotation parameter a, and magnetic parameter B influence their dynamics. We derive analytical expressions for the energy and angular momentum of stable equatorial circular orbits, along with the corresponding radial and latitudinal oscillation frequencies, as functions of M, a, and B. We also examine the key features of the quasi-periodic oscillations (QPOs) of test particles near stable circular orbits, including the precession effects such as periastron precession and the Lense-Thirring effect. We compare our results with those corresponding to the Kerr BH. We find that the particle motion is strongly shaped by the BH parameters. Using a WKB approach, we also study scalar quasinormal modes of rotating KBR BH in an external magnetic field and show that the magnetic field increases damping, while rotation and angular momentum mainly set the oscillation frequencies. Alternatively, general relativistic modeling of Bondi-Hoyle-Lyttleton (BHL) accretion onto rapidly rotating KBR BH shows that two distinct physical structures emerge and cyclically transform into one another over time. These processes produce either a strongly oscillating flip─flop shock cone or a nearly stationary toroidal structure, with their formation governed by the BH spin and magnetic curvature. Power spectral analysis shows that these configurations give rise to low- and high-frequency QPO, providing a unified theoretical framework to understand how multiple QPO─like features can arise in rapidly spinning accreting systems.

The cosmological distribution and formation rate of compact astrophysical objects such as fast radio bursts (FRBs) are typically assumed to be proportional to a linear combination of cosmological star formation rate and stellar mass. In the literature, a template for star formation rate, which is just a function of redshift, is typically used. In this work, we point out the importance of galaxy stellar mass function which captures the host galaxy information of observed FRBs as well as the redshift evolution of galaxy stellar mass. Using this information and taking the stellar mass distribution of a sample of localized FRBs at face value, we find that FRB formation efficiency per stellar mass may have to be more efficient (by a factor of ≍3) than previously calculated, in order to reproduce the observed volumetric rate of FRBs at z = 0. We show that cosmological population studies of FRBs have to include host galaxy information along with its redshift evolution in order to obtain unbiased results. This consideration is also applicable to other transients, e.g. gamma-ray bursts and merging binary black hole events. We show that our approach may open up the possibility to distinguish between different scenarios of merging binary black holes formation with a detection of few thousand gravitational wave events.