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Effective geometries arising from a hypothetical discrete structure ofspace-time can play an important role in the understanding of the gravitationalphysics beyond General Relativity. To discuss this question, we make use oflessons from crystalline systems within solid state physics, where the presenceof defects in the discrete microstructure of the crystal determine the kind ofeffective geometry needed to properly describe the system in the macroscopiccontinuum limit. In this work we study metric-affine theories withnon-metricity and torsion, which are the gravitational analog of crystallinestructures with point defects and dislocations. We consider a crystal-motivatedgravitational action and show the presence of topologically non-trivialstructures (wormholes) supported by an electromagnetic field. Their existencehas important implications for the quantum foam picture and the effectivegravitational geometries. We discuss how the dialogue between solid statephysics systems and modified gravitational theories can provide useful insightson both sides.

The quantum, the geon, and the crystal