Regular nonminimal magnetic black hole as a source of quasiperiodic oscillations

We study the properties of the spacetime around a regular nonminimal magnetic black hole (BH) together with the dynamics of the neutral, magnetized, and magnetically charged particles in its vicinity. The dependence of the values of curvature invariants and the outer event horizon corresponding to the extreme charge of the BH from the coupling parameter are studied in detail. Our study of the test particle motion shows that the innermost stable circular orbit (ISCO) radius decreases with the increase of the magnetic charge of the nonminimal regular magnetic BH. We show that the increase of the ISCO radius with the increase of the coupling parameter is due to the decrease of the extreme value of the BH charge. In particular, when the coupling parameter $q\to \infty$ the ISCO radius tends to the value $r_{\mathrm{ISCO}}=4.5M$. The effect of the magnetic charge parameter on ISCO radius can mimic the effect due to the spin parameter of the rotating Kerr BH, and the mimicking values of the spin parameter decreases with the increase of the coupling parameter. We also explore the possible mimicking of the parameters through the observations of twin-peak quasiperiodic oscillations (QPOs). Our analysis shows that the Reissner-Nordström (RN) charge can mimic the spin parameter of the Kerr BH up to $a/M\simeq 0.51$ provided that there is the same relation between the upper and lower frequencies of the twin-peak QPOs. On the other hand, the nonminimal regular magnetic BH coupling parameter may mimic the spin parameter up to $a/M\simeq 0.215$ in the relativistic precession model.

Figure 1

Radial profiles of scalar invariants of the spacetime (4) for the different values of the nonminimal parameter $q$ and the fixed magnetic charge of the BH $Q_m/M=0.1$. The left, middle, and right panels correspond to the radial dependence of the Ricci scalar, Ricci tensor, and Kretschmann scalar, respectively.

Figure 2

Dependence of the event horizon radius on the magnetic charge of the regular magnetic BH, $Q_m$, for different values of the nonminimal coupling parameter $q$. $q/M^2$ is presented as $q$.

Figure 3

Dependence of (top panel) the minimum value of the outer (event) horizon radius and (bottom panel) the maximum value of the magnetic charge $Q_m$, which allows the BH to exist, on the nonminimal coupling parameter $q$.

Figure 4

The radial dependence of lapse function for the different values of the nonminimal parameter and the corresponding values of the magnetic charge $Q_m\to Q_{\mathrm{extr}}$.

Figure 5

The radial dependence of (top panel) specific angular momentum and (bottom panel) energy for circular orbits for different values of the nonminimal coupling parameter $q$ than the Schwarzschild and RN BH cases.

Figure 6

Dependence of the minimal distance where circular motion is allowed from the magnetic charge of the regular nonminimal BH for different values of the nonminimal coupling parameter ($q/M^2\to q$).

Figure 7

Dependence of the ISCO radius of the neutral massive particles around a regular nonminimal magnetic BH from the magnetic charge of the BH for different values of the nonminimal coupling parameter compared to the RN case.

Figure 8

The degeneracy relations between the spin of the Kerr BH and the magnetic charge of the magnetic regular BH providing the same value of the ISCO radius for different values of the nonminimal coupling parameter $q$.

Figure 9

Dependence of the energy efficiency from the magnetic charge of the regular nonminimal magnetic BH for different values of the nonminimal coupling parameter $q$.

Figure 10

Degeneracy relations between the spin of a rotating Kerr BH and the magnetic charge of the regular nonminimal magnetic BH providing the same value of energy efficiency for different values of the nonminimal coupling parameter $q$.

Figure 11

Radial dependence of the Keplerian frequencies of test particles around an extreme rotating Kerr BH and extremely charged RN and nonminimal magnetic BHs for different values of the nonminimal coupling parameter $q$.

Figure 12

Radial dependence of frequencies of radial oscillations of test particles around an extreme Kerr BH and extremely charged RN and nonminimal magnetic BHs for different values of the nonminimal coupling parameter $q$.

Figure 13

Relations between the frequencies of upper and lower picks of twin-pick QPOs in the RP, WD, and ER2–ER4 models around a Schwarzschild BH, an extremely rotating Kerr BH, and extremely charged RN and nonminimal magnetic BHs for different values of the nonminimal coupling parameter $q$.