Tube dislocations in gravity

TL;DR

This paper investigates static cylindrical shells as sources in Einstein's equations, exploring their mathematical properties, the interplay between elasticity and gravity, and how defects can influence spacetime geometry.

Contribution

It provides explicit solutions for metrics with delta-function energy-momentum tensors and analyzes the connection between defect theory and general relativity.

Findings

Explicit metric components for cylindrical shells are derived.

Ambiguous curvature terms cancel in Einstein's equations.

Elasticity theory offers new insights into spacetime defects.

Abstract

We consider static massive thin cylindrical shells (tubes) as the sources in Einstein's equations. They correspond to $\dl$- and $\dl'$-function type energy-momentum tensors. The corresponding metric components are found explicitly. They are not continuous functions in general and lead to ambiguous curvature tensor components. Nevertheless all ambiguous terms in Einstein's equations safely cancel. The interplay between elasticity theory, geometric theory of defects, and General Relativity is analyzed. The elasticity theory provides a simple picture for defects creation and a new look on General Relativity.