Probing Einstein-Maxwell-Scalar Black hole via Thin Accretion Disks and Shadows with EHT Observations of M87* and Sgr A*

TL;DR

This work analyzes the optical signatures of Einstein-Maxwell-Scalar (EMS) black holes by deriving a static, spherically symmetric EMS solution with a parametric coupling $K(\phi)$ controlled by $\alpha$ and $\beta$, and studying null geodesics, shadows, and thin-disk emission. By comparing the EMS shadow to Event Horizon Telescope (EHT) measurements of M87* and Sgr A*, the authors constrain the EMS parameters and reveal that $\beta$ is more strongly limited than $\alpha$ under current data. They further dissect light bending, transfer functions, and three disk-emission models to show that direct emission dominates observed images, while lensing and photon rings contribute marginally, with the EMS parameters systematically reducing the observed intensity relative to Schwarzschild. Additionally, a weak-lensing analysis via the Gauss-Bonnet theorem yields an approximate deflection angle $\hat{\alpha} \approx \frac{4M}{b}-\frac{3\pi Q^2(1-\alpha^2+\beta)}{4 b^2}$ and corresponding magnification trends, highlighting observational avenues to distinguish EMS spacetimes from GR black holes.

Abstract

We investigated the shadows and thin accretion disks of Einstein-Maxwell-Scalar (EMS) black hole. Firstly, we investigated the influence of EMS parameters on the black hole shadow using the null geodesic method and constrained these parameters based on EHT observations of M87* and Sgr A*. Furthermore, we analyzed the direct emission, lensing ring, and photon ring structures in EMS black hole. Comparing our results with the Schwarzschild and Reissner-Nordstr$\ddot{\mathrm{o}}$m (RN) black holes, we found that the Schwarzschild black hole exhibits the largest shadow radius and the highest observed intensity.

Figures (10)

• Figure 1: The above three pictures plot the function $f(r)$ for different values of $\beta$,$\alpha$ and $q$.
• Figure 2: The above four pictures plot the photon sphere radius under the different parameters $\alpha$, $\beta$ and $q$.
• Figure 3: Example of calculation of light ray emitted from the observer's position into the past under an angle $a$. The BH horizon and the photon sphere are shown; $r_{\mathrm{ph}}$ is the photon sphere radius. The picture is indicated in Ref.176.
• Figure 4: These plots are showing the constraints for different coupling parameters $\alpha$ and $\beta$.
• Figure 5: The behavior of photon trajectories around the Schwarzschild, RN, and EMS BHs as a function of the impact parameter $b$. In the upper panel, we present the total number of orbits, defined as $n = \phi / 2\pi$. The trajectories are categorized based on $n$, where direct emission $n < 3/4$ is shown in black, lensed trajectories $3/4 < n < 5/4$ in yellow, and photon ring trajectories $n > 5/4$ in red. The lower panel displays selected photon trajectories in Euclidean polar coordinates $(r, \phi)$. The spacing in the impact parameter is set to $1/10$, $1/100$, and $1/1000$ for the direct, lensed, and photon ring trajectories, respectively. The BH is represented as a solid disk, while the dashed black circle in the ray-tracing diagram marks the photon orbit. For the three cases studied, we set $\alpha = 0, \beta = 0, q = 0$ for the Schwarzschild BH (first column), $\alpha = 0, \beta = 0, q = 0.5$ for the RN BH (second column), and $\alpha = 0.5, \beta = 0.8, q = 0.5$ for the EMS BH (third column).