Geodesic dynamics and multi-inclination images of a non-minimally coupled black hole with a thin accretion disk

TL;DR

This study analyzes optical signatures of a static regular black hole in non-minimally coupled Einstein–Yang–Mills theory with a Wu–Yang ansatz, illuminated by a thin Keplerian disk. By solving geodesic motion for massive and massless particles, it shows that increasing the non-minimal coupling $\xi$ (and the charge $Q$) reduces the radii of the innermost stable circular orbit $r_{\mathrm{ISCO}}$ and the photon sphere $r_{\mathrm{ph}}$ approximately linearly, while the horizon radius $r_+$ decreases nonlinearly. Using backward ray tracing with an equatorial-emission model, it finds that the non-minimal coupling broadens the allowed range of the critical impact parameter and yields smaller, darker images compared with Schwarzschild and RN spacetimes for the same effective charge. These results suggest observable imprints of non-minimal EYM gravity on black hole shadows and provide a framework for testing such theories with future high-resolution observations, though the simplified disk model used here invites further GRMHD validation.

Abstract

In this paper, we investigate the optical properties of a black hole in non-minimal Einstein-Yang-Mills theory, illuminated by a thin accretion disk composed of free, electrically neutral plasma. In our setup, matter follows stable circular orbits outside the innermost stable circular orbit (ISCO), while inside the ISCO, it rapidly plunges into the black hole. We begin by analyzing the orbital dynamics of massive and massless particles around the black hole. Our results indicate that as the non-minimal coupling parameter increases, the radii of both the ISCO and the photon sphere, together with the corresponding energy and angular momentum for massive particles or the impact parameter for photons, decrease approximately linearly. Moreover, compared with the Schwarzschild and Reissner-Nordström black holes, the non-minimal coupling extends the range of the impact parameter and slightly enhances the redshift effect in the images. Additionally, due to the significant influence of the non-minimal coupling parameter on the event horizon, the observed intensity of the non-minimally coupled black hole image under the selected emission model ultimately turns out to be weaker than that of the other two types of black holes, regardless of the inclination angle between the accretion disk and observation planes.

Figures (19)

• Figure 1: The radii of both the Cauchy and event horizons as functions of $Q$, for $\xi = 0~\text{(RN)}$, $\xi = \frac{1}{3} \xi_{\mathrm{c}}$, $\xi = \frac{2}{3} \xi_{\mathrm{c}}$, and $\xi = \xi_{\mathrm{c}}$, which respectively correspond to the blue dashed, green dot-dashed, orange dotted, and red solid lines.
• Figure 2: The radius, angular momentum, and energy of a particle in the ISCO, as functions of $Q$ with $\xi$ fixed (top row), and as functions of $\xi$ with $Q$ fixed (bottom row).
• Figure 3: The profiles of the energy, angular momentum, and angular velocity of particles in stable circular orbits for the Schwarzschild, RN, and non-minimally coupled black holes.
• Figure 4: The effective potential of photons for the Schwarzschild, RN, and non-minimally coupled black holes.
• Figure 5: The radius of the photon sphere, the critical impact parameter, and the radius of the event horizon, as functions of $Q$ with $\xi$ fixed (top row), and as functions of $\xi$ with $Q$ fixed (bottom row).