Analytical and numerical study of accretion processes around charged spherically symmetric black holes in scalar-tensor Gauss-Bonnet gravity

TL;DR

This work analyzes accretion and geodesic dynamics around a charged, static black hole in scalar-tensor Gauss-Bonnet gravity, focusing on the roles of the GB coupling $c_1$ and the cosmological constant $\Lambda$. It combines analytic geodesic calculations (including ISCO, E, L, and epicyclic frequencies) with GRHD simulations of Bondi-Hoyle-Lyttleton accretion to study how modified gravity alters orbital stability, radiation flux, and shock-cone morphology. The main findings show that larger $c_1$ and more negative $\Lambda$ weaken gravitational focusing, modify the shock cone structure, reduce accretion efficiency and density inside the cone, and damp oscillations, implying a transition to more stable accretion flows. These results suggest that observable properties of accretion disks and quasi-periodic oscillations can serve as probes to constrain scalar-tensor Gauss-Bonnet gravity in strong-field regimes, providing a bridge between theory and high-resolution astrophysical observations.

Abstract

We investigate the physical phenomena occurring around a spherically symmetric, non-rotating charged black hole (BH) to explore the effects of scalar-tensor Gauss-Bonnet gravity on circular motion, accretion disk properties, and Bondi-Hoyle-Lyttleton (BHL) accretion flow. By analytically and numerically examining the influence of the Gauss-Bonnet coupling constant $c_1$ and the cosmological parameter $Λ$, we reveal how these modified gravity parameters alter the underlying physical processes. Using geodesic analysis, we compute the specific energy, angular momentum, innermost stable circular orbit (ISCO) radius, and radiation flux of test particles, providing insight into how the modified gravity framework affects orbital stability and the organization of the accretion flow. Subsequently, through numerical solutions of the general relativistic hydrodynamic (GRHD) equations, we describe the morphology of the shock cone formed via the BHL accretion mechanism around the BH. The numerical results demonstrate that increasing the values of $c_1$ and negative $Λ$ reduce gravitational focusing. Consequently, depending on the parameter choices, the opening angle of the shock cone either widens or narrows compared to the Schwarzschild case. However, because of weakened gravitational focusing, both the amount of accreted matter and the density of material trapped inside the cone decrease significantly. These results indicate that scalar-tensor Gauss-Bonnet corrections act as an effective gravitational damping term, transferring turbulence and transforming shock-dominated accretion into more stable configurations. The consistency between theoretical and numerical results suggests that the observable properties of accretion disks and quasi-periodic oscillations (QPOs) can serve as probes to constrain the parameters of scalar-tensor Gauss-Bonnet gravity in strong-field regimes.

Figures (14)

• Figure 1: The graph displays the horizons of the CBH, represented by $B(r)$, according to the radial coordinate $r$. It shows the variation in horizons for different values of the parameters $M$, $c_1$ and $\Lambda$.
• Figure 2: The graph shows the variation of the effective potential $V_{eff}$ of the CBH according to $r$, considering different values of $c_1$ and $\Lambda$.
• Figure 3: The graph illustrates the variation of the specific energy $E$ of the CBH with respect to $r$ for different values of $c_1$ and $\Lambda$.
• Figure 4: The graph illustrates the variation of angular momentum $L$ of the CBH with respect to $r$ for different values of $c_1$ and $\Lambda$.
• Figure 5: The graph illustrates the variation of $Z(r)$ of the CBH with respect to $r$ for different values of $c_1$ and $\Lambda$.