Relativistic accretion process onto rotating black holes in Einstein-Euler-Heisenberg nonlinear electrodynamic gravity

TL;DR

The paper investigates how Einstein-Euler-Heisenberg (EEH) nonlinear electrodynamics alters accretion and oscillations around rotating black holes. It combines analytical treatment of equatorial circular orbits and epicyclic frequencies with GR hydrodynamics simulations of Bondi-Hoyle-Lyttleton accretion in EEH backgrounds to map $V_{eff}$, orbital frequencies, and precession. Key findings show that the EEH charge $\tilde{Q}$ and spin $a$ modify horizon structure, enhance inner-disk high-frequency QPOs and generate a robust two-zone accretion pattern with strong near-horizon instabilities and suppressed outer turbulence, yielding observable QPO signatures such as near-integer resonances. These QPO patterns provide a testable diagnostic of EEH gravity in the strong-field regime with horizon-scale imaging and X-ray timing, potentially observable by missions like NICER, Athena, and eXTP.

Abstract

In this study, we uncover the accretion dynamics and oscillatory behavior around rotating black holes within the EEH nonlinear electrodynamic framework by analyzing both the motion of test particles and numerically solving the general relativistic hydrodynamic equations. Using EEH geometry, we compute the structure of circular motion, the effective potential and force, and we evaluate the orbital, radial, and vertical epicyclic frequencies together with the Lense-Thirring and periastron precession rates. Our calculations show that, compared to the Kerr model, the charge parameter $Q$ and the spin parameter $a$ significantly modify the strong gravitational field and shift the characteristic frequencies. We then model the dynamical structure formed by matter accreting toward the EEH black hole through the BHL mechanism, finding that the parameter $Q$ increases the amount of infalling matter and strengthens shock-cone instabilities near the horizon, while farther from the black hole it suppresses accretion and reduces turbulence. Time-series analysis of the accretion rate reveals robust QPOs, whose low-frequency components arise from the precession of the shock cone, while high-frequency components appear as a consequence of strong-field instabilities modified by $Q$ and $a$. A systematic parameter-space exploration identifies the regions where EEH corrections maximize QPO activity, indicating that nonlinear electrodynamics can leave observable imprints on accretion flows and may be testable with QPO and horizon-scale observations.

Figures (22)

• Figure 1: Variation of the horizon radii ($r_{\pm}/M$) in the EEH metric as a function of the charge-to-mass ratio ($Q$) for different values of the BH spin parameter ($a$). As $a$ increases, the admissible range of $Q$ that yields a regular BH solution becomes narrower, whereas values of $Q$ outside this range correspond to the formation of a naked singularity .
• Figure 2: Pictorial representation of energy of particles around rotating EEH BH.
• Figure 3: Plots of angular momentum of particles around rotating EEH BH.
• Figure 4: Effective potential for particles around rotating EEH BH.
• Figure 5: Variation of the effective force acting on test particles around a rotating EEH BH for different values of the magnetic parameter $B$ and spin parameter $a$.