Solitonic generation of vacuum solutions in five-dimensional General Relativity

TL;DR

This paper introduces a solitonic solution-generating method for five-dimensional General Relativity, enabling systematic derivation of axially symmetric vacuum solutions, including black rings, and analyzes their geometric and physical features.

Contribution

It develops a new solitonic technique to generate five-dimensional vacuum solutions from four-dimensional reductions, expanding the toolkit for higher-dimensional gravity research.

Findings

Generated solutions include the $S^2$-rotating black ring.

Analyzed features like conical singularities and closed timelike curves.

Explored the relation between different coordinate representations.

Abstract

We describe a solitonic solution-generating technique for the five-dimensional General Relativity. Reducing the five-dimensional problem to the four-dimensional one, we can systematically obtain single-rotational axially symmetric vacuum solutions. Applying the technique for a simple seed solution, we have previously obtained the series of stationary solutions which includes $S^2$-rotating black ring. We analyze the qualitative features of these solutions, e.g., conical singularities, closed timelike curves, and spacetime curvatures. We investigate the rod structures of seed and solitonic solutions. We examine the relation between the expressions of the metric in the prolate-spheroidal coordinates and in the C-metric coordinates.