MG12 - Talk detail
 

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Einstein-Rosen waves and the self-similarity hypothesis in cylindrical symmetry

The self-similarity hypothesis claims that in classical general relativity, spherically symmetric solutions may naturally evolve to a self-similar form in certain circumstances. We investigate self-similar vacuum solutions to the Einstein equation in the so-called whole-cylinder symmetry. We find that those solutions are reduced to part of the Minkowski spacetime if the homothetic vector is orthogonal to the axis. Then, as we generalize the analysis, we find a two-parameter family of self-similar vacuum solutions, where the homothetic vector is not orthogonal to the axis in general. The family includes the Minkowski, the Kasner and the cylindrical Milne solutions. These solutions describe the interior to the exploding (imploding) shell of gravitational waves or the collapse (explosion) of gravitational waves in general. This means that the self-similarity hypothesis is naturally generalized to cylindrical symmetry.

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