Real-time creation of curved space-time for gravitational lensing in phononic crystals

We propose a method to generate an artificial curved space-time metric that mimics the metric at the vicinity of a black hole. This metric supports the gravitational lensing phenomenon, describing the deflection of light beams around the event horizon. Our model is based on the quantum condensed matter formalism for Weyl semimetals with an inhomogeneous circular potential, resulting in space-dependent tilted dispersion cones. We numerically realize a classical analogue of this quantum system by inducing active feedback interactions in a two-dimensional square phononic crystal. The feedback mechanism is necessary to generate the non-reciprocal Weyl Hamiltonian couplings in the classical dynamical matrix.