  We show that tilted Weyl semimetals with a spatially varying tilt of the Weyl
cones provide a platform for studying analogues to problems in anisotropic
optics as well as curved spacetime. Considering particular tilting profiles, we
numerically evaluate the time evolution of electronic wave packets and their
current densities. We demonstrate that electron trajectories in such systems
can be obtained from Fermat's principle in the presence of an inhomogeneous,
anisotropic effective refractive index. On the other hand, we show how the
electrons dynamics reveal gravitational features and use them to simulate
gravitational lensing around a synthetic black hole. These results bridge
optical and gravitational analogies in Weyl semimetals, suggesting novel
pathways for experimental solid-state electron optics.
