EinsteinRosen waves and the selfsimilarity hypothesis in cylindrical symmetry
Harada, Tomohiro and Nakao, Kenichi and Nolan, Brien C. (2009) EinsteinRosen waves and the selfsimilarity hypothesis in cylindrical symmetry. Physical Review D, 80 (2). 0240251. ISSN 15507998 Full text available as: AbstractThe selfsimilarity hypothesis claims that in classical general relativity, spherically symmetric solutions may naturally evolve to a selfsimilar 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 selfsimilar vacuum solutions to the Einstein equation in the socalled wholecylinder symmetry. We find that those solutions are reduced to part of the Minkowski spacetime with a regular or conically singular axis and with trivial or nontrivial topology if the homothetic vector is orthogonal to the cylinders of symmetry. These solutions are analogous to the Milne universe, but only in the direction parallel to the axis. Using these solutions, we discuss the nonuniqueness (and nonvanishing nature) of C energy and the existence of a cylindrical trapping horizon in Minkowski spacetime. Then, as we generalize the analysis, we find a twoparameter family of selfsimilar vacuum solutions, where the homothetic vector is not orthogonal to the cylinders in general. The family includes the Minkowski, the Kasner, and the cylindrical Milne solutions. The obtained solutions describe the interior to the exploding (imploding) shell of gravitational waves or the collapse (explosion) of gravitational waves involving singularities from nonsingular initial data in general. 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 selfsimilarity hypothesis is naturally generalized to cylindrical symmetry. Download statisticsArchive Staff Only: edit this record
