Motion of particles in a magnetically charged Euler-Heisenberg black hole with scalar hair

Abstract: We study the geodesic motion of uncharged particles in the background of a magnetically charged Euler-Heisenberg black hole with a scalar hair. The spacetime can be asymptotically (A)dS or flat and we find, analysing the behavior of the effective potential of the radial motion that in all cases there exist stable and unstable orbits. Performing numerical integrations we depict the motion of particles for planetary and critical orbits, as well as for radial geodesics. We discuss the effect that the scalar hair $\nu$, the magnetic charge $Q_{m}$ and the Euler-Heisenberg parameter $\alpha$ have on the particle motion.