  To simulate the dynamics of massless Dirac fermions in curved spacetimes with
one, two, and three spatial dimensions we construct tight-binding Hamiltonians
with spatially varying hoppings. These models represent tilted Weyl semimetals
where the tilting varies with position, in a manner similar to the light cones
near the horizon of a black hole. We illustrate the gravitational analogies in
these models by numerically evaluating the propagation of wave packets on the
lattice and then comparing them to the geodesics of the corresponding curved
spacetime. We also show that the motion of electrons in these spatially varying
systems can be understood through the conservation of energy and the
quasi-conservation of quasimomentum. This picture is confirmed by calculations
of the scattering matrix, which indicate an exponential suppression of any
noncontinuous change in the quasimomentum. Finally, we show that horizons in
the lattice models can be constructed also at finite energies using specially
designed tilting profiles.

Mesoscale and Nanoscale Physics