Influence of plasma on the observational appearance of rotating black holes in Horndeski gravity

TL;DR

The paper investigates how a surrounding plasma environment affects the shadow of rotating hairy Horndeski black holes, using the Hamilton-Jacobi formalism to derive photon trajectories in both uniform and non-uniform plasmas. It analyzes unstable spherical photon orbits and computes celestial coordinates for several plasma profiles, showing that homogeneous plasma tends to enlarge the shadow while non-homogeneous plasmas shrink it and can erase it at high densities. The hair parameter $h$ enhances shadow size and distortion in the homogeneous case, and the authors constrain the plasma parameters ($k_0$, $k_r$, $k_\theta$) by fitting the Horndeski BH shadow to the EHT observation of M87* with inclination $\theta_o=17^{\circ}$. The results demonstrate that rotating Horndeski BHs can describe the observed shadow within specific plasma parameter ranges, highlighting the viability of using shadow observations to probe both modified gravity and plasma environments around black holes.

Abstract

Exploring the influence of plasma on the light rays trajectories in the vicinity of black holes is significat since that astrophysical black holes are generally surrounded by a plasma medium. In this work, we analyze the null geodesics in the space-time of rotating hairy Horndeski black holes immersed in a plasma medium using the Hamilton-Jacobi method. By considering both uniform and non-uniform plasma distributions, we perform a comparative study of their effects on the black hole shadow. The impact of the hair parameter and the inclination angle on the black hole shadow is also investigated. Finally, the shadow results are compared with observational data of the Event Horizon Telescope for M87* to constrain the plasma parameter.

Figures (6)

• Figure 1: The behavior of horizons of the rotating Horndeski BH for $a=0.9M$ with different values of $h$ parameter. The solid curve corresponds to the Kerr BH.
• Figure 2: Horndeski BH shadows with various plasma parameters $k_0$, $k_r$ and $k_{\theta}$: homogeneous plasma distribution with $\omega_p^2= k_0\omega_0^2$ (left panel), inhomogeneous distribution with $\omega_p^2 = \frac{k_r\sqrt{r}}{r^2+a^2\cos^2\theta}\omega_0^2$ (middle panel) and with $\omega_p^2 = \frac{k_{\theta}(1+2\sin^2\theta)}{r^2+a^2\cos^2\theta}\omega_0^2$ (right panel). In each panel the solid curve corresponds to the vacuum case. The inclination angle is set to $\theta_{\rm o}=\frac{\pi}{2}$.
• Figure 3: Horndeski BH shadows in homogeneous plasma distribution for different inclinations angles with $a=0.9M$ and $h=-0.2M$ (left panel), different spin parameter with $h=-0.2M$ and $\theta_{\rm o}=\frac{\pi}{2}$ (middle panel), and for different Horndeski parameter with $a=0.9M$ and $\theta_{\rm o}=\frac{\pi}{2}$ (right panel). The homogeneous plasma parameter is set to $k_0=0.2$.
• Figure 4: The shadow diameter for the rotating hairy Horndeski BH as a function of homogeneous plasma parameter $k_{0}$, for fixed $a=0.9M$ and different values of hair parameter (left panel), and for fixed $h=-0.1M$ and different values of rotation parameter (right panel), with $\theta_{\rm o}=17^{\circ}$. In each panel the shaded area shows the observationally diameter of M87* shadow, within $1\sigma$ and $2\sigma$ confidence intervals.
• Figure 5: The shadow diameter for the rotating hairy Horndeski BH as a function of radial plasma parameter $k_{r}$, for fixed $a=0.9M$ and different values of hair parameter (left panel), and for fixed $h=-0.1M$ and different values of rotation parameter (right panel), with $\theta_{\rm o}=17^{\circ}$. In each panel the shaded area shows the observationally diameter of M87* shadow, within $1\sigma$ and $2\sigma$ confidence intervals.