Geodynamics and artificial gravity in spacetime crystals under slow perturbation and deformation

We present a theory of geodynamics in a spacetime crystal based on an event wave packet constructed from the Floquet-Bloch waves, which involves not only a scalar dispersion function but also a Berry curvature tensor in the phase space manifold of spacetime and the reciprocal quasi-energy-momentum. In the presence of structural deformation, this theory is naturally extended into a covariant form with the introduction of a lattice connection constructed out of the gradients of the local lattice vectors. This geometric framework reveals three distinct gravitational forces: lattice deformation gravity, dispersion gravity, and Berry curvature gravity. These forces manifest as distinct, experimentally tunable connection and metric terms in the geodynamics, establishing a framework for engineering artificial spacetime by controlling lattice strain, band structure, and wave function topology. Our work provides a direct conceptual link between general relativity and condensed matter physics, opening a path toward the laboratory realization of novel gravitational phenomena.