Recent advances in non-linear electrodynamics (NLED) and analogue gravity

In this talk, I will discuss recent advances connecting NLED, analogue gravity, and emergent spacetime structures. I will first introduce the idea that small electromagnetic perturbations in a nonlinear theory propagate according to an optical metric, whose causal cones depend on the background field.

I will then present three complementary developments: the construction of photon traps in NLED, an analogue model of a rotating black hole, and a more recent geometrical result involving the full principal symbol of the theory. Together, these results suggest that nonlinear electromagnetic media can provide not only analogues of black-hole kinematics, but also a controlled framework for exploring causality, wave propagation, and quantum-field-theoretic ideas beyond the geometrical-optics limit.