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https://doi.org/10.1140/epjc/s10052-022-10357-2

Regular Article - Theoretical Physics

## Investigating strong gravitational lensing effects by supermassive black holes with Horndeski gravity

^{1}
Centre for Theoretical Physics, Jamia Millia Islamia, 110025, New Delhi, India

^{2}
Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag 54001, 4000, Durban, South Africa

^{b}
shafphy@gmail.com

Received:
25
December
2021

Accepted:
22
April
2022

Published online:
14
May
2022

We study gravitational lensing in strong-field limit by a static spherically symmetric black hole in quartic scalar field Horndeski gravity having additional hair parameter *q*, evading the no-hair theorem. We find an increase in the deflection angle ${\alpha}_{D}$, photon sphere radius ${x}_{\mathit{ps}}$, and angular position ${\theta}_{\infty}$ that increases more quickly while angular separation *s* more slowly, but the ratio of the flux of the first image to all other images ${r}_{\mathit{mag}}$ decreases rapidly with increasing magnitude of the hair *q*. We also discuss the astrophysical consequences in the supermassive black holes at the centre of several galaxies and note that the black holes in Horndeski gravity can be quantitatively distinguished from the Schwarzschild black hole. Notably, we find that the deviation $\mathrm{\Delta}{\theta}_{\infty}$ of black holes in Horndeski gravity from their general relativity (GR) counterpart, for supermassive black holes Sgr A* and M87*, for $q=-0.2$, respectively, can reach as much as $2.4227\phantom{\rule{3.33333pt}{0ex}}\mu $as and $1.82026\phantom{\rule{3.33333pt}{0ex}}\mu $as while $\mathrm{\Delta}s$ is about $0.04650\phantom{\rule{3.33333pt}{0ex}}\mu $as for Sgr A* and $0.03493\phantom{\rule{3.33333pt}{0ex}}\mu $as for M87*. The ratio of the flux of the first image to all other images suggest that the Schwarzschild images are brighter than those of the black holes in Horndeski gravity, wherein the deviation $|\mathrm{\Delta}{r}_{\mathit{mag}}|$ is as much as 0.70673. The results suggest that observational tests of hairy black holes in Horndeski gravity are indeed feasible. Taking the supermassive black holes Sgr A* and M87* as the lens, we also compare our hairy Horndeski black holes observable signatures with those of the neutral Horndeski black holes, Galileon black holes and charged Horndeski black holes. It turns out that although it is possible to detect some effects of the strong deflection lensing by the hairy Horndeski black holes and other black holes with the Event Horizon Telescope (EHT) observations, but it is unconvincing to discern these black holes as deviations are $\mathcal{O}(\mu $as). We also find that the shadow size is consistent with EHT observation if the deviation parameter $q\in (-0.281979,0)$

*© The Author(s) 2022*

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