Symmetry in Nonlinear Mathematical Physics - 2009

Mikhail Katanaev (Steklov Mathematical institute, Moscow, Russia)

Tube dislocations in gravity

We consider static massive thin cylindrical shells (tubes) as the sources in Einstein's equations. They correspond to d- and d-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.