Tube dislocations in gravity

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.

27 pages, 3 figures

References in corpus (6)

• Geometric Theory of Defects
• Distributional Energy-Momentum Tensor of the Kerr-Newman Space-Time Family
• The Ultrarelativistic Kerr-Geometry and its Energy-Momentum Tensor
• Scattering on Dislocations and Cosmic Strings in the Geometric Theory of Defects
• One-dimensional topologically nontrivial solutions in the Skyrme model
• Inside the BTZ black hole

Cited by in corpus (7)

• Magnetic branes in Gauss-Bonnet gravity with nonlinear electrodynamics: correction of magnetic branes in Einstein-Maxwell gravity
• Three dimensional magnetic solutions in massive gravity with (non)linear field
• Magnetic brane solutions of Lovelock gravity with nonlinear electrodynamics
• Disclinations in the geometric theory of defects
• Magnetic solutions in Einstein-massive gravity with linear and nonlinear fields
• Torsional Elastic Waves in Double Wall Tube
• Trajectories in a space with a spherically symmetric dislocation