Gravitational lensing of Euler-Heisenberg black hole surrounded by perfect fluid dark matter

In this work, we study the gravitational lensing of Euler-Heisenberg black hole surrounded by perfect fluid dark matter. This kind of black hole solution enables us to investigate the nontrivial interplay between the dark matter effects and nonlinear electrodynamics effects (or quantum electrodynamics effects) on charged black hole systems. The important observables in gravitational lensings are calculated and discussed in our work, including the gravitational deflection angle of light and time delay of light. Additionally, we also explore the massive orbit’s bound orbits (and their precession angles) and black hole shadow radius for Euler-Heisenberg black hole in the presence of dark matter. The results indicate that the Euler-Heisenberg black hole with a larger perfect fluid dark matter parameter could greatly reduce the gravitational deflection angle of light, time delay of light and precession angle of massive object’s bound orbit, while the nonlinear electrodynamics effects do not have large influences on these observables.