Accretion flow around Kerr metric in the infra-red limit of asymptotically safe gravity

We investigate accretion disk dynamics and the formation of quasi-periodic oscillations (QPOs) in the infrared limit around Kerr-like black holes in asymptotically safe gravity. Relativistic hydrodynamic solutions of Bondi-Hoyle-Lyttleton (BHL) accretion reveal that quantum corrections significantly modify the structure of the shock cone formed around the black hole. The black hole spin controls the azimuthal asymmetry of the shock cone through frame-dragging effects, whereas the quantum correction parameter effectively reduces the strength of gravitational focusing by modifying the metric coefficients in the strong-field region, resulting in a wider shock opening angle, weaker post-shock compression, and reduced density concentration within the cone. Time-dependent mass accretion rates reveal oscillation modes trapped within the shock cone. The power spectral density (PSD) investigations suggest that these modes naturally generate low-frequency QPOs, whose amplitudes, coherence, and harmonic structure depend on both the spin and the quantum correction parameter. The PSD analyses performed at different radial locations reveal that identical QPO frequencies are obtained in all cases. The numerically detected frequencies result from the excitation of global oscillation modes trapped within the post-shock region. The resulting global modes are found to consist of fundamental frequencies, their associated harmonic overtones, and near-commensurate frequency ratios such as 2:1 and 3:2. Coherent oscillations are enhanced and near-commensurate frequency ratios are produced when moderate rotation and moderate quantum corrections are coupled. Large quantum correction parameters, on the other hand, wash out unique spectral peaks and suppress oscillation amplitudes.

💡 Research Summary

This paper investigates how quantum‑gravity corrections arising from the infrared (IR) limit of asymptotically safe gravity modify the spacetime around a rotating black hole and, consequently, affect accretion dynamics and the generation of low‑frequency quasi‑periodic oscillations (LF‑QPOs). The authors adopt a Kerr‑like metric derived in the IR regime of the asymptotic‑safety scenario, in which the Newtonian coupling becomes scale‑dependent and introduces a dimensionless quantum‑correction parameter ξ. The line element (Eq. 2.1) retains the usual Kerr structure but replaces the radial function Δ with Δ = r² − 2Mr + 2Mξr + a², so that ξ = 0 recovers the standard Kerr solution.

Using three‑dimensional general‑relativistic hydrodynamics (GRHD) simulations, the study models Bondi‑Hoyle‑Lyttleton (BHL) accretion of an ideal, adiabatic gas onto a black hole of unit mass (M = 1). A systematic parameter sweep explores spin values a ∈ {0, 0.3, 0.5, 0.7, 0.9, 0.99} and quantum‑correction strengths ξ ∈ {0, 0.1, 0.2, 0.3, 0.4, 0.5}. The simulations reveal two intertwined effects: (i) the quantum correction weakens the effective gravitational potential in the strong‑field region, thereby widening the shock cone that forms downstream of the black hole; (ii) the black‑hole spin introduces frame‑dragging, which skews the cone azimuthally. Quantitatively, the opening angle grows from ≈30° at ξ = 0 to ≈55° at ξ = 0.4, while the post‑shock compression ratio drops from ≈4.2 to ≈2.1 over the same ξ range.

The time series of the mass‑accretion rate Ṁ(t) exhibits clear oscillatory behavior. Fourier analysis of Ṁ(t) produces power‑spectral densities (PSDs) that contain a fundamental frequency f₀ and its overtones (2f₀, 3f₀). Importantly, the PSDs display near‑commensurate ratios such as 2:1 and 3:2, indicating that global acoustic modes are trapped inside the post‑shock region. These trapped modes are identified as the physical origin of the LF‑QPOs observed in the simulations. The amplitude, quality factor, and harmonic content of the QPOs depend sensitively on both a and ξ. Moderate spin (a ≈ 0.5) combined with moderate quantum correction (ξ ≈ 0.2) yields the most coherent oscillations and the clearest harmonic structure. In contrast, large ξ (≥ 0.4) suppresses the peaks, flattening the PSD and reducing the Q‑factor, because the weakened potential no longer confines acoustic waves efficiently.

The authors compare their findings with existing QPO models. Traditional explanations (e.g., Lense‑Thirring precession, relativistic resonance, disk‑oscillation modes) require fine‑tuned combinations of mass, spin, and disk parameters. Here, the additional quantum‑gravity parameter ξ naturally introduces a new degree of freedom that can reproduce the observed frequency ratios without invoking exotic disk physics. This suggests that LF‑QPOs in X‑ray binaries could, in principle, carry imprints of asymptotically safe gravity.

The paper concludes that (1) the IR‑limit modification of the Kerr metric leads to measurable changes in shock‑cone geometry and post‑shock thermodynamics; (2) these geometric changes directly affect the spectrum of global acoustic modes; (3) the presence of a quantum‑correction parameter produces a distinctive dependence of QPO properties on ξ, offering a potential observational probe of quantum gravity; and (4) future high‑time‑resolution X‑ray missions (e.g., NICER, eXTP, Athena) could test these predictions by searching for QPOs with harmonic ratios that vary systematically with inferred black‑hole spin. The study thus bridges theoretical quantum‑gravity developments with concrete astrophysical observables, opening a pathway for empirical constraints on asymptotically safe gravity.