Near-horizon polarized images of a rotating hairy Horndeski black hole

TL;DR

The paper investigates near-horizon polarization of light from a rotating Horndeski black hole with scalar hair, focusing on how the hair parameter $h$ affects the EVPA. By modeling equatorial plasma flows with ideal conductivity and computing the Penrose-Walker constant, the authors show that the leading EVPA is set by spacetime geometry (as in Kerr), while hair introduces a measurable, subleading correction via the horizon angular velocity $\Omega_h$. The results demonstrate that the hair parameter increases or decreases the observed EVPA depending on the spin regime and that the effect is modulated by the azimuthal polarization angle and observer inclination. The work highlights the potential of near-horizon polarization as a probe of Horndeski hair and, more broadly, black hole no-hair theorems, motivating high-precision observations in future very-long-baseline interferometry.

Abstract

Recently, Hou \emph{et al.} [Astrophys. J. Lett. \textbf{988}, L51 (2025)] revealed that the Electric Vector Position Angle (EVPA) of polarization vectors in the near-horizon images is governed solely by the spacetime geometry and is irrespective of the plasma flows. Here, we generalize the study to the scenario of a rotating hair black hole within the Horndeski gravity and probe the effects of the hairy parameter on the EVPA. For a fixed inclination, the hairy parameter enhances the observed EVPA in the slowly rotating case, but decreases it in the rapidly rotating case. For a fixed black hole spin, the influence of the hairy parameter on the observed EVPA under different observer inclinations is further modulated by the azimuthal angle of the observed polarization vector. The hairy parameter's impact is more distinct in the low inclination case as the azimuthal angle lies within a specific range, but is almost independent of the observer inclination as the azimuthal angle is beyond this specific range. Furthermore, the dependence of the hairy parameter's impact on the EVPA is stronger with respect to the black hole spin than to the inclination angle. These results could help to further understand the near-horizon polarized images and Horndeski gravity.

Figures (5)

• Figure 1: Variation of the function $\Delta{(r)}$ with the radial coordinate $r$ for different black hole hair parameters. The black hole spins in the left and right panels are set to $a=0.2$ and $a=0.94$, respectively. Here set $M=1$.
• Figure 2: Variation of the critical value $h_c$ with the spin $a$ for rotating hair black holes within the Horndeski gravity. Here set $M=1$.
• Figure 3: Variation of $z$ with $\Delta$ for three different types of plasma flows in the rotating hairy Horndeski black hole spacetime. The left and right panels correspond to spin parameters $a=0.2$ and $a=0.94$, respectively. Each panel in the bottom row is a partial enlargement of the respective panel in the upper row.
• Figure 4: Variation of the EVPA in the near-horizon images with the azimuthal angle $\phi$ in the rotating hairy Horndeski black hole spacetime. The left panel is for $\theta_o=17^{\circ}$ and the right one is for $\theta=80^{\circ}$. In each panel, the solid and dashed lines correspond to the cases $h=h_c$ and $h=0$, and the blue and red lines denote the cases $a=0.94$ and $a=0.2$, respectively.
• Figure 5: EVPA in the near-horizon images of rotating hairy Horndeski black holes with different symbols: $\bullet$ indicates $\chi=\frac{\pi}{6}$, and $\triangle$ indicates $\chi=-\frac{\pi}{6}$. The left panel is for $a=0.2$ and the right one is for $a=0.94$. In each panel, the curves represent the near-horizon images. The solid and dashed lines correspond to the cases $h=h_c$ and $h=0$, and the blue and red lines denote the cases $\theta_o=17^{\circ}$ and $\theta_o=80^{\circ}$, respectively.