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

TL;DR

This work studies accretion dynamics and quasi-periodic oscillations around Kerr-like black holes in the infrared limit of asymptotically safe gravity. Using GRHD simulations of Bondi-Hoyle-Lyttleton accretion on the IR-modified Kerr background, it shows that the quantum correction parameter $\\xi$ weakens the effective gravity, broadening the shock cone and lowering post-shock density, while black hole spin induces asymmetry through frame-dragging. The resulting low-frequency QPOs are global, trapped modes whose amplitudes and harmonic content depend on $a$ and $\\xi$, with near-commensurate ratios (e.g., 2:1, 3:2) emerging for moderate values of both parameters. Importantly, the QPO frequencies scale with black hole mass as $f(M)=f_{10}(10 M_\\odot / M)$, enabling applications from X-ray binaries to active galactic nuclei and offering a diagnostic for infrared-modified gravity in strong-field regimes.

Abstract

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 asymmetric of the shock cone through frame-dragging effects, whereas the quantum correction parameter softens the effective gravitational potential, 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.

Figures (8)

• Figure 1: Variation of the outer ($r_{+}$, solid lines) and inner ($r_{-}$, dashed lines) black hole horizons as a function of the quantum correction parameter $\xi$ for the Kerr metric in the infra-red limit of asymptotically safe gravity. The horizons are shown separately for each black hole spin parameter $a = 0$, $0.5$, and $0.9\,M$, as listed in Table \ref{['Initial_data']}. An increase in $\xi$ causes the inner and outer horizons to approach each other and eventually merge at a critical value, beyond which no horizon exists.
• Figure 2: Color and contour plots of the shock cone and plasma structure formed via the BHL mechanism around a Kerr black hole in the infrared limit of asymptotically safe gravity are presented. Each panel corresponds to a different model listed in Table \ref{['Initial_data']}. The variation of the shock cone and its morphology in the strong gravitational field is shown for different values of the black hole spin parameter $a$ and the quantum correction parameter $\xi$. In addition, the velocity field is illustrated by vector plots, revealing the inflow of matter toward the black hole and the flow structure within and around the shock cone.
• Figure 3: Left panel: The azimuthal variation of the density of the shock cone formed around the black hole, computed at $r = 2.66M$, i.e., very close to the black hole horizon. The profiles are shown for different values of the spin parameter $a$ and the quantum correction parameter $\xi$, and are also plotted for the corresponding Schwarzschild and Kerr models with the same spin values for comparison. Right panel: Variation of the normalized shock cone opening angle as a function of $\xi$ for different spin configurations. The shock opening angle is normalized with respect to the corresponding Schwarzschild or Kerr case for each spin value, thereby highlighting deviations from the classical black hole models.
• Figure 4: Numerical results for the mass accretion properties of the quantum-corrected Kerr black hole in the infra-red limit of asymptotically safe gravity. Top panel: The time evolution of the mass accretion rate $dM/dt$ computed at the location closest to the black hole horizon, $r = 2.3M$, is shown for different values of the spin parameter $a$ and the quantum correction parameter $\xi$, together with the Schwarzschild and Kerr cases, after the shock cone reaches a quasi-steady state. Bottom left panel: The mean mass accretion rate $\langle \dot{M} \rangle$ calculated from the corresponding accretion rate shown in the top panel. The error bars represent the standard deviation of temporal fluctuations. Bottom right panel: The model-dependent variation of the fractional RMS variability, which quantifies the relative strength of fluctuations in the accretion rate for each model.
• Figure 5: Numerical results for the mass accretion properties of the quantum-corrected Kerr black hole in the infra-red limit of asymptotically safe gravity. The figure is the same as Fig.\ref{['acc_r23']}, but in this case the mass accretion rate $dM/dt$, the mean accretion rate $\langle \dot{M} \rangle$, and the fractional RMS variability are computed at $r = 6.11M$, corresponding to the vicinity of the ISCO.