Tube dislocations in gravity

Abstract

We consider static massive thin cylindrical shells (tubes) as the sources in Einstein’s equations. They correspond to δ- and δ′-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 defect creation and a new look on general relativity.