Using precession and Lense-Thirring effect to constrain a rotating regular black hole

TL;DR

We address the strong-field behavior of a rotating regular black hole with a Minkowski core by focusing on frame-dragging and spin precession signatures. Our approach combines analytic derivations of equatorial epicyclic frequencies and gyroscope precession in the rotating regular BH spacetime with a data-driven constraint from X-ray QPOs via Markov Chain Monte Carlo. The main findings are a tight bound $α/M^{3/2} < 0.60$ (95% C.L.) from five QPO events, and a consistent picture in which nonzero $α$ suppresses LT, geodetic, and generalized spin-precession frequencies relative to Kerr, with pronounced anisotropy in inclination. These results demonstrate the viability of using QPOs and gyroscope precession as probes of quantum-gravity corrections to black-hole spacetimes and outline paths for tighter tests with future X-ray observatories.

Abstract

In this paper, we investigate the frame-dragging effect on an accretion disk and test gyroscope orbiting around a rotating regular black hole with a Minkowski core. Firstly, we perturb a bound timelike circular orbit around the black hole, and analyze the periastron precession and Lense-Thirring (LT) precession frequencies of the orbit's epicyclic oscillations. Since these epicyclic oscillations can be used to explain the quasiperiodic oscillations (QPOs) phenomena of the accretion disc around this rotating regular black hole, we then employ the Markov Chain Monte Carlo (MCMC) simulation to fit our theoretical results with five QPOs events (GRO J1655-40, GRS 1915+105, XTE J1859+226, H1743-322 and XTE J1550-564). The simulations give the relevant physical parameter space of the black hole, including the characteristic radius $r$, the mass related parameter $M$, the spinning parameter $a$ and the quantum gravity effect $α$. The results give the constraint on the quantum effect parameter, with an upper limit $α/M^{3/2} < 0.60$ at the $95\%$ C.L., which is tighter than $<0.7014$ in our pervious study within static case. Then, we theoretically explore the LT precession frequency, geodetic precession frequency, and the general spin precession frequency of a test gyro attached to a stationary observer in this black hole background. We find that the quantum gravity effect suppresses the precession frequencies comparing against those in Kerr black hole, further providing a theoretical diagnostic of the potential quantum gravity effect.

Figures (6)

• Figure 1: The radial profiles of $\nu_{\text{nod}}$ and $\nu_{\text{per}}$ for selected parameters. Upper panel: $\nu_{\text{nod}}$ and $\nu_{\text{per}}$ with $a=0,~0.3M,~0.5M$ when $\alpha=0.6M^{2/3}$; Bottom panel:$\nu_{\text{nod}}$ and $\nu_{\text{per}}$ with $\alpha=0,~0.6M^{2/3},~0.9M^{2/3}$ when $a=0.4M$.
• Figure 2: Constraints on the parameters of the rotating regular black hole with GRO J1655–40 from current observations of QPOs within the relativistic precession model.
• Figure 3: Constraints on the parameters of the rotating regular black hole with GRS 1915+105, XTE J1859+226, H1743-322 and XTE J1550-564 from current observations of QPOs within the relativistic precession model.
• Figure 4: Lense-Thirling precession frequency as a function of radial coordinate for rotating regular black hole. In plot (a), we check the effect of the black hole spin with $\alpha=0.6 M^{2/3},\ \theta=\pi/2$; In plot (b), the figure shows the effect of the angle with $a=0.2M, \alpha=0.6 M^{2/3}$; And in plot (c), we check the effect of the regular black hole parameter $\alpha$ with fixed $a=0.2M,\ \theta=\pi/2$.
• Figure 5: The geodetic precession as a function of radial coordinate for a static regular black hole. The left panel desplays $\Omega_{\text{geodetic}}$ for different values of $\alpha$, while the right panel represents the deviation of $\Omega_{\text{geodetic}}$ from the corresponding Schwarzschild black hole with the same parameters.