Space-time as strongly bent plate

TL;DR

This paper develops a multidimensional elastic plate model of space-time, deriving equilibrium equations and comparing it with general relativity, to explore alternative geometric and physical interpretations.

Contribution

It introduces a multidimensional elasticity theory framework for space-time, deriving new equilibrium equations and analyzing its relation to general relativity.

Findings

Derived general equilibrium equations for space-time as an elastic plate.

Compared multidimensional elasticity theory with general relativity.

Reviewed variational principles and boundary conditions in this context.

Abstract

Futher development is made of a consept of space-time as multidimensional elastic plate, proposed earlier in [20,21]. General equilibrium equations, including 4-dimensional tangent stress tensor - energy-momentum tensor of matter - are derived. Comparative analysis of multidimensional elasticity theory (MET) and GR is given. Variational principle, boundary conditions, energy-momentum tensor, matter and space-time signature are reviewed within the context of MET.