Euler-Heisenberg Black Holes in Einsteinian Cubic Gravity

We explore black hole solutions and some of its physical properties in Einstein's theory in 4D, modified by a cubic gravity term and in the presence of non-linear electrodynamics. In the context of Effective Field Theories (EFT) and under certain assumptions, these curvature and non-linear electromagnetic terms represent the first corrections to the Einstein-Maxwell theory. We obtain static and spherically symmetric generalizations to the asymptotically flat Reissner-Nordstr\"om metric using perturbative methods, showing how an asymptotic expansion solution connects with a near horizon solution for a small coupling of the curvature correction term. Finally, we discuss how these EFT corrections change the event horizon properties and also lead to measurable effects on black hole shadows and gravitational lensing around these solutions.