Spacetime as a deformable solid

TL;DR

This paper explores the idea of modeling spacetime as a deformable solid with a fundamental lattice, deriving Einstein's equations from this analogy and suggesting the metric is secondary.

Contribution

It introduces a novel approach to spacetime by treating it as a deformable body with a lattice structure, leading to Einstein's equations from this perspective.

Findings

Spacetime can be modeled as a deformable lattice.

Einstein equations emerge from spacetime deformations.

Spacetime metric is a secondary object.

Abstract

In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define an fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction. We simulate the spacetime manifold by a very specific congruence of curves and use the Landau-Raychadhuri equation to study the behavior of such a congruence. The lattice appears because we are forced to associate to each curve of the congruence a sort of fundamental "particle". The world-lines of these particles should be identified with the congruence fulfilling the spacetime manifold. The conclusion is that when describing the deformations of the spacetime the Einstein equations emerge and the spacetime metric should be treated as a secondary (not fundamental) object of the theory.