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

TL;DR

This paper investigates black hole shadows, quasinormal modes, and optical appearances within Horndeski theory, using EHT data to constrain theory parameters and analyze observational features.

Contribution

It provides the first detailed analysis of BH shadows and QNMs in Horndeski theory, constrained by EHT observations of M87* and Sgr A*.

Findings

EHT observations constrain Horndeski theory parameters.

Frequency ranges of fundamental QNMs are determined.

Current EHT resolution mainly captures direct emission from BHs.

Abstract

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 $\mathrm{Sgr} \mathrm{A}^*$.