The quantum, the geon, and the crystal

TL;DR

This paper explores how discrete space-time structures inspired by crystalline defects can lead to effective geometries in gravity, revealing topologically non-trivial solutions like wormholes supported by electromagnetic fields.

Contribution

It introduces a crystal-inspired gravitational action within metric-affine theories, demonstrating the emergence of wormholes and linking solid state physics concepts to quantum gravity models.

Findings

Existence of wormhole solutions supported by electromagnetic fields.

Analogies between crystalline defects and gravitational geometries.

Insights into quantum foam and effective space-time structures.

Abstract

Effective geometries arising from a hypothetical discrete structure of space-time can play an important role in the understanding of the gravitational physics beyond General Relativity. 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 non-metricity 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 non-trivial 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.