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The quantum, the geon and the crystal. (English) Zbl 1339.83061

Summary: Effective geometries arising from a hypothetical discrete structure of spacetime can play an important role in the understanding of the gravitational physics beyond General Relativity (GR). To discuss this question, we make use of lessons from crystalline systems within solid state physics, where the presence of defects in the discrete microstructure of the crystal determine the kind of effective geometry needed to properly describe the system in the macroscopic continuum limit. In this work, we study metric-affine theories with nonmetricity and torsion, which are the gravitational analog of crystalline structures with point defects and dislocations. We consider a crystal-motivated gravitational action and show the presence of topologically nontrivial structures (wormholes) supported by an electromagnetic field. Their existence has important implications for the quantum foam picture and the effective gravitational geometries. We discuss how the dialogue between solid state physics systems and modified gravitational theories can provide useful insights on both sides.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
53Z05 Applications of differential geometry to physics
82D25 Statistical mechanics of crystals
83C45 Quantization of the gravitational field
83C27 Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory
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