Infinite Number of Stationary Soliton Solutions to Five-dimensional Vacuum Einstein Equation

TL;DR

This paper constructs an infinite family of stationary soliton solutions to the five-dimensional vacuum Einstein equations using inverse scattering, revealing new solutions including a variant of the Myers-Perry black hole.

Contribution

It introduces a method to generate an infinite set of soliton solutions with explicit characterization, expanding the known solution space of five-dimensional Einstein equations.

Findings

The (2,0)-soliton solution matches the Myers-Perry black hole with one angular momentum.

The (2,2)-soliton solution differs from the black ring solution, despite some metric components being similar.

An infinite number of solutions are characterized by two soliton numbers and a normalization constant.

Abstract

We obtain an infinite number of soliton solutions to the 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 related to a coordinate condition. We show that the (2,0)-soliton solution is identical to the Myers-Perry solution with one angular momentum by imposing a condition 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 metric of two metrics can be identical.