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

We obtain an infinite number of soliton solutions to the the five-dimensionalstationary Einstein equation with axial symmetry by using the inversescattering method. We start with the five-dimensional Minkowski space as a seedmetric to obtain these solutions. The solutions are characterized by twosoliton numbers and a constant appearing in the normalization factor related toa coordinate condition. We show that the (2,0)-soliton solution is identical tothe Myers-Perry solution with one angular momentum by imposing a conditionbetween parameters. We also show that the (2,2)-soliton solution is differentfrom the black ring solution discovered by Emparan and Reall, although onecomponent of the metric of two metrics can be identical.Comment: 13 page