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

Anzhuoer Li1,2,*, Liang Dong3,†, and Qian Niu1

  • *Contact author: leean@utexas.edu
  • †Contact author: liangdong@utexas.edu
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Phys. Rev. Research 8, 013028 – Published 14 January, 2026

DOI: https://doi.org/10.1103/ybht-9k5h

Abstract

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.

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Phys. Rev. Research 8, 013028– Published 14 January, 2026
  • Received 27 October 2023
  • Accepted 13 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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