Distinguishing black holes from string-inspired Euler–Heisenberg theory through shadow images

Recently, an interesting doppelgänge black hole solution was obtained in the string-inspired Euler–Heisenberg theory, this solution describes black holes that have the same horizon radii but different charges. However, we find that they possess different ISCOs and photon spheres, and hence these differences affect their shadow images. In this work, we investigate the optical appearances of such black holes illuminated by an optically and geometrically thin disk. We find that doppelgänge black holes have different optical appearances. Doppelgänger black holes with identical event horizon radii but different charges cast unequal shadows, demonstrating that the nonlinear charge affects the spacetime structure beyond the horizon. Furthermore, we find that black holes with large magnetic charge [Formula: see text] produce novel shadow images where the usual bright rings outside the shadow become indistinct. The optical appearances illuminated by spherically symmetric accretion are also examined, these appearances allow us to distinguish between the two doppelgänger black holes.