Effect of primary scalar hair on black hole's strong lensing in Beyond Horndeski Gravity

TL;DR

This paper investigates how primary scalar hair affects black hole strong lensing in Beyond Horndeski gravity, using observational data to constrain the scalar hair parameter and analyzing the stability of these models.

Contribution

It provides new constraints on scalar hair parameters from strong lensing observations and discusses the stability and observational limitations of such black hole models.

Findings

Constraints on scalar hair from Event Horizon Telescope data

Black hole shadow corresponds to secondary accretion disk image

Models with constrained scalar hair exhibit local instabilities

Abstract

We study the gravitational lensing effects of a static, asymptotically flat black hole with primary scalar hair in Beyond Horndeski gravity, focusing on the strong lensing regime. Recently, in Ref. [1], we placed constraints on the scalar hair parameter by analyzing its thermodynamic stability and the black hole shadow. In this work, we further investigate the strong lensing properties of the black hole, which form the basis of shadow formation, and employ observational data from the Event Horizon Telescope to derive more precise constraints on the scalar hair parameter. Additionally, we compute the shape and position of different lensed images of a thin accretion disk and argue that the observed black hole shadow corresponds to the secondary image of the emitting disk. Using this interpretation, we perform a new set of constraints on the scalar hair. Furthermore, we discuss why higher-order images are not suitable for astrophysical constraints, highlighting the limitations posed by their faintness and observational challenges. Finally, we find that models satisfying these constraints exhibit local instabilities.