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

Abstract 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. We also analyze in detail the case of extremal BH spacetimes and we find that the radius of both the event horizon and shadow exhibits discontinuities when varying with respect to either the magnetic charge or the scalar charge. These extremal scenarios exist for sufficiently small values of the EH parameter, and imply the formation of a second photon ring around the BH shadow. Upon comparing the theoretically calculated BH shadow to the images of the shadows of M87* and Sgr A* observed by the Event Horizon Telescope collaboration, we impose constraints on the BH parameters, namely the scalar hair (ν), the magnetic charge (Q₌ Q m) and the EH parameter (α). For sufficiently large values of the EH parameter, our model is in agreement with the EHT observations for approximately every value for the BH magnetic charge.