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.