Shadows, Quasinormal Modes, and Optical Appearances of Black Holes in Horndeski Theory

This work describes the motion of photons in black hole (BH) spacetimes within the framework of Horndeski theory. We focus on the shadows, quasinormal modes (QNMs) and optical appearances of BHs surrounded by geometrically thin accretion disks. The QNMs of BHs are calculated by the WKB method and the eikonal limit, respectively. Using Event Horizon Telescope (EHT) observations of $\mathrm{M} 87^*$ and $\mathrm{Sgr} \mathrm{A}^*$, we can constrain the parameter in Horndeski theory to a small range. Based on the constraint, we obtain the frequency ranges of the fundamental modes for $\mathrm{M} 87^*$ and $\mathrm{Sgr} \mathrm{A}^*$ in Horndeski theory. By exploring the optical appearances of BHs, we find that for the current resolution of the EHT, it primarily captures direct emission. This work advances our understanding of the observational characteristics of BHs in Horndeski theory and constrains Horndeski theory by EHT observations of $\mathrm{M} 87^*$ and $\mathrm{Sgr} \mathrm{A}^*$.