Shadow of Bonanno-Reuter Black Hole in Plasma Medium: Insights from EHT Sgr A* Observations

Abstract

We investigate the properties of black hole shadows in the renormalization group (RG) improved Bonanno-Reuter spacetime, incorporating quantum gravitational corrections via the scale-dependent parameter $(\tildeω)$ in a plasma medium. Light propagation in a non-uniform, pressureless plasma with a radial density profile is analyzed through modified equations of motion. The black hole shadow angular radius is computed, and its dependence on $\tildeω$ and the plasma index is analyzed. The analysis of specific limiting cases indicates systematic deviations of the black hole shadow relative to the classical Schwarzschild limit. Using Event Horizon Telescope (EHT) observations of Sgr~A*, we place constraints on $\tildeω$. Furthermore, within the considered parameter range, plasma and quantum-gravity effects exhibit an observational degeneracy, which future high-resolution measurements with the next-generation EHT are expected to break, thereby providing tighter constraints on the model parameters.

Figures (6)

• Figure 1: Variation of the metric function with radial distance for different values of $\gamma$, considering (a) $M=2$ and (b) $M=3$. We set $G_{0}=1$ and $\gamma=4.5$.
• Figure 2: Variation of radius of photon sphere as a function of $\gamma$ for different values of $h$. Parameters are chosen as $M=5$, $G_{0}=1$, $k_{p}=0.5$, and $\tilde{\omega} = 118/(15\pi)$.
• Figure 3: Schematic representation of photon deflection near a BH surrounded by a plasma medium. $\alpha_{sh}$ is the angular radius of the shadow Bisnovatyi-Kogan:2017kiiRoy:2025hdw.
• Figure 4: The angular shadow radius of the BRBH: (a) for different values of the QG correction parameter $\tilde{\omega}$, with the plasma index fixed at $h = 1$ and $\gamma = 4.5$; (b) for different values of the plasma index parameter $h$, with $\tilde{\omega} = 0.5$ and $\gamma = 4.5$ fixed. Here, $x/M$ and $y/M$ denote the angular celestial coordinates on the observer’s sky, normalized by the BH mass $M$ (or equivalently by the shadow radius $R_{\rm sh}/M$).
• Figure 5: Comparison of the shadows of the BRBH and SBH, each computed in both vacuum and in the presence of a plasma medium. The parameters are chosen as $M=1$ for the SBH, $M=2$ for the BRBH, $G_0=1$, $\tilde{\omega}=0.5$, plasma density falloff index $h=3$ where applicable, and the parameter $\gamma=4.5$ fixed for the BRBH. Here, $X$ and $Y$ denote the angular celestial coordinates on the observer’s sky, normalized by the BH mass $M$ (or equivalently by the shadow radius $R_{\rm sh}/M$).