Motion of particles around a magnetically charged Euler-Heisenberg black hole with scalar hair and the Event Horizon Telescope

We study the motion of uncharged particles and photons in the background of a magnetically charged Euler-Heisenberg (EH) black hole (BH) with scalar hair. The spacetime can be asymptotically (A)dS or flat. After investigating particle motions around the BH and the behavior of the effective potential of the particle radial motion, we determine the contribution of the BH parameters to the geodesics. Photons follow null geodesics of an effective geometry induced by the corrections of the EH non-linear electrodynamics. Thus, after determining the effective geometry, we calculate the shadow of the BH. Upon comparing the theoretically calculated BH shadow with the images of the shadows of M87* and Sgr A* obtained by the Event Horizon Telescope collaboration, we impose constraints on the BH parameters, namely the scalar hair (\(\nu\)), the magnetic charge (\(Q_{m}\)) and the EH parameter (\(\alpha\)).