Dynamics, Ringdown, and Accretion-Driven Multiple Quasi-Periodic Oscillations of Kerr-Bertotti-Robinson Black Holes

Abstract

We study the motion of test particles around 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 of test particles near stable circular orbits, including the precession effects such as periastron precession and the Lense-Thirring effect. Finally, we compare our results with those corresponding to the Kerr BH. We find that particle motion is strongly shaped by the BH parameters. Using a WKB approach, we also study scalar quasinormal modes of a 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 modelling of Bondi-Hoyle-Lyttleton (BHL) accretion onto a 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 black hole spin and magnetic curvature. Power spectral analysis shows that these configurations give rise to low and high-frequency quasi-periodic oscillations, offering a unified explanation for the multiple quasi-periodic oscillations observed in rapidly spinning X--ray binaries.

Figures (18)

• Figure 1: Energy of test particles in equatorial circular orbits around a rotating KBR BH, shown as a function of radial distance $r/M$. The left panel illustrates the influence of the magnetic parameter $B$ for a fixed spin $a/M = 0.3$; the right panel shows the effect of the spin parameter $a$ for a fixed magnetic parameter $B^2 M^2 = 0.6$.
• Figure 2: Specific angular momentum $\mathcal{L}/M$ of test particles in equatorial circular orbits around a rotating KBR BH. The left panel displays the dependence on the magnetic parameter $B$ for fixed $a/M = 0.3$; the right panel shows the variation with spin $a$ for fixed $B^2 M^2 = 0.3$.
• Figure 3: Effective potential $V_{\text{eff}}/M$ for test particles moving in the equatorial plane of a rotating KBR BH. The left panel shows the effect of the magnetic parameter $B$ for fixed $a/M = 0.5$ and $\mathcal{L}/M = 2$; the right panel shows the effect of the spin parameter $a$ for fixed $B^2 M^2 = 0.6$ and $\mathcal{L}/M = 2$.
• Figure 4: Fundamental frequencies of small harmonic oscillations for neutral particles around a rotating KBR BH, measured by a distant observer. The plots show the radial $\nu_r$, latitudinal $\nu_\theta$, and azimuthal $\nu_\phi$ frequencies as functions of radial coordinate $r/M$, for different values of the spin parameter $a$ and magnetic parameter $B$..
• Figure 5: Dependence of the fundamental QNM frequencies on the multipole number $l$ for a massless scalar perturbation in the KBR spacetime, assuming a weak magnetic field $B = 0.0005$. The left panel shows the real part $\omega_R$, the right panel shows the imaginary part $\omega_I$.