| Einstein-Rosen waves and the self-similarity hypothesis in cylindrical symmetry (2008) | |||||||||
Abstract | |||||||||
| The self-similarity hypothesis claims that in classical general relativity spherically symmetric solutions may naturally evolve to a self-similar form in certain circumstances. In this context, the validity of the corresponding hypothesis in nonspherical geometry is very interesting as there may exist gravitational waves. We investigate self-similar vacuum solutions to the Einstein equation in cylindrical symmetry. We find that those solutions are reduced to the Minkowski spacetime with a regular or conically singular axis and with trivial or nontrivial topology if the homothetic vector is orthogonal to the axis. Using these solutions, we discuss the nonuniquess (and non-vanishing nature) of $C$-energy and the existence of a cylindrical trapping horizon in Minkowski spacetime. 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. These solutions describe the line explosion of gravitational waves. Since recent numerical simulations strongly suggest that one of these solutions may describe the asymptotic behavior of gravitational waves from the collapse of a dust cylinder, this means that the self-similarity hypothesis is naturally generalized to cylindrical symmetry.. Comment: 16 pages, 3 figures, submitted to PRD | |||||||||
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