Four Dimensional Elasticity and General Relativity

TL;DR

This paper explores a four-dimensional elasticity framework to model space-time, showing it can replicate aspects of general relativity and offering new insights into the geometry and dynamics of the universe.

Contribution

It introduces a novel four-dimensional elasticity theory that describes space-time and connects it with general relativity, including equilibrium equations and symmetry analyses.

Findings

The elastic medium can recover the Minkowski metric under uniaxial stress.

Spherical and cylindrical symmetries are analyzed, showing similarities and differences with classical GR.

The theory suggests a new perspective on the dynamics of space-time as an elastic medium.

Abstract

It has been shown that the extension of the elasticity theory in more than three dimensions allows a description of space-time as a properly stressed medium, even recovering the Minkowski metric in the case of uniaxial stress. The fundamental equation for the metric in the theory is shown to be the equilibrium equation for the medium. Examples of spherical and cylindrical symmetries in four dimensions are considered, evidencing convergencies and divergencies with the classical general relativity theory. Finally the possible meaning of the dynamics of the four dimensional elastic medium is discussed.