Magnetized particle motion and accretion process with shock cone morphology around a decoupled hairy black holes

TL;DR

The study tackles magnetized-particle dynamics and relativistic accretion around a decoupled hairy black hole produced by extended geometric deformation. It derives a new solution with deformation parameters α and β, analyzes magnetized particle motion and circular orbits without imposing standard horizons, and develops a comprehensive accretion framework including sonic points and disk emissivity. Analytically, it shows that increasing α (and related β adjustments) weakens the gravitational potential, shifts ISCOs toward the horizon, enhances near-horizon emissivity, and broadens the shock cone. The results are corroborated by GRHD simulations, which reveal observable shifts in shock-cone morphology and QPO frequencies across the 10–70 Hz band, suggesting concrete observational tests for these hairy BH geometries in X-ray timing and gravitational-wave data.

Abstract

Relativistic accretion onto compact objects such as black holes and neutron stars is one of the most efficient known mechanisms for converting gravitational potential energy into radiation. In the case of rapidly spinning black holes, up to $40\%$ of the rest-mass energy of accreting matter can be released, far exceeding the efficiency of nuclear fusion. In this work, we investigate magnetized particle motion and relativistic accretion processes around a decoupled hairy black hole via extended geometric deformation. The developed geometry involves two hairy parameters that preserve the horizon structure with the additional feature of the fulfillment of weak energy conditions outside the event horizon. We provide the foundation with necessary formalism for magnetized particle motion around a decoupled black hole. The effective potential and innermost stable circular orbits are then derived, which demonstrate a significant reduction of the radius of the latter quantity under the hairy parameters for the magnetized particle. Afterwards, we obtain exact analytical expressions for radial velocity profiles, mass accretion rates, and a few others which reveal improved energy efficiency and emissivity as compared to the standard black hole. Furthermore, the decoupling parameter shows strong influence on oscillations, accretion presenting fantastic agreement between analytical predictions and numerical simulations, and thus offering noticeable observational signatures for future gravitational wave and X-ray astronomy.

Figures (25)

• Figure 1: Theory concerning the variation of the horizon of a decoupled BH with respect to parameters $M$, $\alpha$, and $\beta$. The changes in mass $M$ and the characteristics of the BH $\alpha$ change the color of the event horizon to blue. For any mass $M$ and Hairy parameters $\alpha$ and $\beta$, all solution curves in the display lack inner and outer horizons.
• Figure 2: Changes in magnetic field caused by variations in independent parameters $\alpha$ and $\beta$.In both plots, the magnetic field strength grew as $\alpha$ increased and $\beta$ decreased away from the singularity. Although these graphs have an important role in the magnetic field model, they only show minor changes in the decoupled parameters.
• Figure 3: Variation in Magnetic coupling parameter $\eta$ is due to the variation of decoupled parameters $\alpha$ and $\beta$. $\eta$ increased away from the singularity for increasing the parameters $\alpha$ and $\beta$.
• Figure 4: The changes in the specific energy of the magnetized particle parameter $\zeta$ are attributed to variations in the decoupled parameters $\alpha$ and $\beta$. Near the singularity, $\eta$ decreases as the parameter $\alpha$ increases, while it rises when moving away from the singularity.
• Figure 5: The changes in the minimal value of the magnetic coupling parameter $\eta$ are attributed to variations in the decoupled parameters $\alpha$ and $\beta$. As the parameters $\alpha$ and $\beta$ increase, $\eta_{\text{min}}$ rises as it moves away from the singularity, whereas it decreases as it approaches the singularity.