Shadow and Optical Imaging in Einstein-Maxwell-Dilaton Black Hole

TL;DR

This work analyzes photon trajectories, shadows, and photon/lensing rings of Einstein-Maxwell-dilaton black holes with magnetic charge $q$, using static and infalling spherical accretion as well as optically thin thin-disk models. By deriving the EMD metric and computing $r_h$, $r_p$, and $b_p$, the authors connect spacetime hair to observable features and constrain $q$ with EHT data, finding $q \lesssim 0.826$ ($1\sigma$) and $q \lesssim 0.995$ ($2\sigma$). Across spherical accretion scenarios, the shadow radius is governed by geometry and decreases with increasing $q$, while infalling motion introduces Doppler-darkening inside the shadow; in thin-disk accretion, direct emission dominates the observed flux and ring emissions are magnified yet narrow, with the shadow boundary depending on the emission model. The results suggest that current EHT observations place meaningful, though not definitive, bounds on $q$, and future multi-messenger probes could break degeneracies between EMD and RN geometries while testing modified gravity effects.

Abstract

This paper investigates photon motion in black hole of Einstein-Maxwell-dilaton theory, exploring black hole shadows and observational characteristics under various accretion models. We first give the relation of the event horizon, photon sphere, and critical impact parameter in terms of the magnetic charge $q$. We then use the Event Horizon Telescope data to constrain $q$. For the two spherical accretion models, the infalling scenario yields a darker shadow due to the Doppler effect. However, the shadow radius remains unchanged for different models. In the case of an optically thin, geometrically thin disk accretion model, the observed brightness is predominantly determined by direct emission. The lensing ring provides a secondary contribution to the intensity, whereas the photon ring's emission is negligible. The widths of the lensing and photon rings exhibit a positive correlation with the magnetic charge $q$. Additionally, within the disk model framework, the black hole shadow radius is found to depend on the specific emission model.

Figures (14)

• Figure 1: Left panel: Effective potential for the SC BH, RN BH, and EMD BH. Right panel: Magnified view of the effective potential near the extremum.
• Figure 2: Left panel: The relationship between the photon sphere radius $r_p$ of the EMD black hole and the hair parameter $q$. Right panel: The relationship between the critical impact parameter $b_p$ and the parameter $q$. The right panel utilizes the mass-to-distance ratio prior from EHT observations of $Sgr A^*$, combining data from $Keck$ and $VLTI$ after averaging. The green region represents the 1$\sigma$ confidence interval, the white region represents the 2$\sigma$ interval, and the blue region is excluded as it exceeds 2$\sigma$.
• Figure 3: Light ray trajectories in the equatorial plane. From left to right are the SC BH, RN BH, and EMD BH. The black solid circle represents the event horizon, the gray dashed circle represents the photon ring; the red curves correspond to light rays with an impact parameter $b < b_p$; the green curves correspond to light rays with an impact parameter $b > b_p$.
• Figure 4: The distribution of the integrated intensity $F_{\text{obs}}$ with respect to the impact parameter $b$ for the three black holes under the static spherical accretion model. The blue, red, and black curves correspond to the SC BH, RN BH, and EMD BH, respectively.
• Figure 5: The two-dimensional images of black hole shadows and photon rings under the static spherical accretion model. From left to right: SC BH, RN BH, EMD BH.