Non-commutative inspired black holes in Euler–Heisenberg non-linear electrodynamics

Abstract

We find non-commutative inspired electrically and magnetically charged black hole solutions in Euler–Heisenberg non-linear electrodynamics. We analyse the weak energy condition and show that it is satisfied in opposition to the commutative case. We also obtain the shadow associated with these metrics that may be susceptible to observation. Keywords: Euler–Heisenberg non-linear electrodynamics, Non-commutative smeared distributions, Shadow of a black hole, Energy conditions