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Prog. Theor. Phys. Vol. 116 No. 2 (2006) pp. 319-328

An Infinite Number of Stationary Soliton Solutions to the Five-Dimensional Vacuum Einstein Equation

Takahiro Azuma^1,* and Takao Koikawa^2,**

¹Department of Languages and Culture, Dokkyo University, Soka 340-0042, Japan
²School of Social Information Studies, Otsuma Women's University, Tama 206-0035, Japan

(Received January 4, 2006)

Abstract:

We obtain an infinite number of soliton solutions to the five-dimensional stationary Einstein equation with axial symmetry by using the inverse scattering method. We start with the five-dimensional Minkowski space as a seed metric to obtain these solutions. The solutions are characterized by two soliton numbers and a constant appearing in the normalization factor which is related to a coordinate condition. We show that the (2,0)-soliton solution is identical to the Myers-Perry solution with one angular momentum variable by imposing a condition on the relation between parameters. We also show that the (2,2)-soliton solution is different from the black ring solution discovered by Emparan and Reall, although one component of the two metrics can be identical.

URL : http://ptp.ipap.jp/link?PTP/116/319/
DOI : 10.1143/PTP.116.319

^*E-mail: azuma@dokkyo.ac.jp
^**E-mail: koikawa@otsuma.ac.jp

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References:

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 118 No. 1 (2007) pp. 35-46 :

   An Infinite Number of Static Soliton Solutions to the 5D Einstein-Maxwell Equations

   Takahiro Azuma and Takao Koikawa

2. Progress of Theoretical Physics Vol. 121 No. 3 (2009) pp. 627-646 :

   An Infinite Number of Static Soliton Solutions to the 5D Einstein-Maxwell Equations with a Dilaton Field

   Takahiro Azuma and Takao Koikawa

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