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Classification of an infinite series of static solutions to the vacuum Einstein equations |
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| Authors: | Takahiro Azuma Takao Koikawa |
| Affiliation: | (1) Faculty of Liberal Arts, Dokkyo University, 340 Soka, Saitama, Japan;(2) Department of Physics, Tokyo Metropolitan University, Minami-Ohsawa, 1-1, 192-03 Hachioji-Shi, Tokyo, Japan;(3) Present address: School of Social Infomation Studies, Otsuma Women's University, 9-1 Kamioyamada-Machi, 206 Tama, Tokyo, Japan |
| Abstract: | We propose a classification of an infinite series of the static solutions to the vacuum Einstein equation by means of their soliton number and the real and/or complex pole trajectories. We also show that in the 4-soliton solution there appears an intriguing ring solution of which the curvature invariant has a finite limit at the rings. |
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