Infinite number of soliton solutions to 5-dimensional vacuum Einstein equation

TL;DR

This paper presents an infinite family of exact solutions to the 5-dimensional static vacuum Einstein equations with axial symmetry, including the recently discovered static black ring, using the inverse scattering method.

Contribution

It introduces an infinite set of solutions characterized by soliton numbers, expanding the known solution space for 5D vacuum Einstein equations.

Findings

Includes the static black ring solution as a special case.

Demonstrates the use of inverse scattering method for generating solutions.

Provides a systematic way to generate multiple solutions with soliton parameters.

Abstract

We give an infinite number of exact solutions to the 5-dimensional static Einstein equation with axial symmetry by using the inverse scattering method. The solutions are characterized by two integers representing the soliton numbers. The first non trivial example of these solutions is the static black ring solution found recently.