  Here, we show that isorefractive spacetime crystals with a travelling-wave
modulation may mimic rigorously the response of moving material systems. While
generic spacetime crystals are characterized by a bi-anisotropic coupling in
the co-moving frame, isorefractive crystals have a response that is observer
independent, which leads to isotropic constitutive relations free of
bianisotropy. We show how to take advantage of this property in the calculation
of the band diagrams of isorefractive spacetime crystals in the laboratory
frame and in the study of the synthetic Fresnel drag. Furthermore, we discuss
the impact of considering either a Galilean or a Lorentz transformation in the
homogenization of spacetime crystals, showing that the effective response is
independent of the considered transformation.
