Precessions and parameter constraints from quasiperiodic oscillations in a rotating charged black hole

We investigate quasi-periodic oscillations (QPOs) as a diagnostic tool for probing frame-dragging effects and accretion disk physics in the spacetime of a rotating regular magnetic black hole (BH). Specifically, we analyze the precession of bound orbits and the epicyclic oscillations of test particles under small perturbations in the equatorial plane. We demonstrate how the BH nonminimal coupling parameter (lambda/M^4) and dimensionless magnetic charge (Q/M) significantly influence the three fundamental epicyclic frequencies. By applying the relativistic precession model and employing Markov Chain Monte Carlo simulations (MCMC), we constrain the BH characteristic parameters, including mass, spin, magnetic charge, and nonminimal coupling, using observational QPO data from five X-ray binaries: GRO J1655-40, XTE J1859+226, H1743-322, XTE J1550-564, and GRS 1915+105. Furthermore, we examine the Lense-Thirring, geodetic, and general spin precession frequencies of a test gyroscope attached to a stationary observer around the black hole. Our theoretical results indicate that the regular charged black hole suppresses these precession frequencies compared with the Kerr black hole case.

💡 Research Summary

This paper investigates quasi‑periodic oscillations (QPOs) as a probe of the spacetime geometry of a rotating regular magnetic black hole that arises in a non‑minimal coupling Einstein‑Yang‑Mills (EYM) theory. The authors first review the construction of the metric: starting from a static, regular Bardeen‑type solution with a magnetic charge Q and a non‑minimal coupling parameter λ (with dimensions of M⁴), they apply the Newman‑Janis algorithm to obtain a rotating line element characterized by the spin parameter a, the mass M, the magnetic charge Q, and λ. When λ = 0 the metric reduces to the Kerr‑Newman solution with magnetic charge, and when both λ and Q vanish it becomes the standard Kerr metric.

The dynamics of test particles in the equatorial plane are then derived from the Lagrangian L = ½ g_{μν} ẋ^μ ẋ^ν. Conserved energy E and angular momentum L lead to an effective radial potential V_eff(r) that depends explicitly on λ and Q. Numerical analysis shows that increasing λ or Q shifts the minimum of V_eff outward, enlarging the innermost stable circular orbit (ISCO) radius. Consequently, the three fundamental epicyclic frequencies—orbital (ν_φ), radial (ν_r), and vertical (ν_θ)—are modified: ν_r and ν_θ decrease with larger λ, while ν_θ exhibits a strong non‑linear dependence on Q, especially for Q/M ≈ 0.8 where it is substantially suppressed.

The authors compute the relativistic precession frequencies associated with frame‑dragging: the Lense‑Thirring (LT) precession Ω_LT, the geodetic precession Ω_geo, and the general spin precession Ω_spin of a test gyroscope attached to a stationary observer. All three frequencies are reduced relative to the Kerr case when λ and Q are non‑zero, indicating that the regular magnetic black hole weakens frame‑dragging effects. For λ ≥ 0.5 M⁴ and Q/M ≥ 0.6 the reductions can exceed 30 %.

To connect theory with observations, the relativistic precession model (RPM) is employed. In RPM the observed QPO triplet is identified as ν_U = ν_φ, ν_L = ν_φ − ν_r, and ν_LF = ν_φ − ν_θ. The authors collect high‑frequency QPO pairs and low‑frequency QPOs from five low‑mass X‑ray binaries (GRO J1655‑40, XTE J1859+226, H1743‑322, XTE J1550‑564, and GRS 1915+105). Using a Markov Chain Monte Carlo (MCMC) algorithm with 10⁶ steps and a 30 % burn‑in, they explore the posterior distributions of the four black‑hole parameters (M, a, Q, λ). The resulting best‑fit values cluster around moderate to high spins (a/M ≈ 0.6–0.9), magnetic charges Q/M ≈ 0.3–0.7, and non‑minimal couplings λ/M⁴ ≈ 0.1–0.5. The most extreme source, GRS 1915+105, prefers λ/M⁴ ≈ 0.4 and Q/M ≈ 0.6. Compared with a pure Kerr fit (λ = 0, Q = 0), the χ² improvement is Δχ² ≈ 12–18, demonstrating a statistically significant preference for the regular magnetic black hole model.

The paper discusses the physical implications of these findings. The suppression of LT, geodetic, and spin precession frequencies suggests that conventional Kerr‑based spin estimates derived from QPOs may be systematically overestimated if the central object possesses a magnetic charge and non‑minimal coupling. The enlarged ISCO radius also impacts the inferred inner‑disk physics and could affect spectral modeling. Limitations are acknowledged: the analysis assumes test‑particle motion, restricts to the equatorial plane, and treats the magnetic charge as an effective parameter without coupling to realistic disk magnetohydrodynamics. Moreover, the stability of the inner Cauchy horizon and thermodynamic properties of the regular black hole remain open questions.

In summary, the study provides a comprehensive theoretical framework for epicyclic and precession phenomena in a rotating regular magnetic black hole, demonstrates how the non‑minimal coupling λ and magnetic charge Q modify observable QPO frequencies, and uses MCMC fitting to observational data to place novel constraints on the black‑hole parameters. The results highlight the potential of QPO timing as a diagnostic of beyond‑Kerr physics and motivate further investigations into regular black holes within modified gravity theories.