Yang-Mills Inspired Solutions for General Relativity

TL;DR

This paper presents new exact solutions to Einstein's vacuum equations derived from Yang-Mills theory, revealing a novel connection between gauge theories and general relativity with distinct physical properties.

Contribution

It introduces a method to generate Einstein's solutions from Yang-Mills solutions, highlighting a novel link between these theories and expanding the solution space.

Findings

Exact cylindrically symmetric solutions to Einstein's equations

Solutions derived from Yang-Mills monopole configurations

Distinct physical characteristics from original Yang-Mills solutions

Abstract

Several exact, cylindrically symmetric solutions to Einstein's vacuum equations are given. These solutions were found using the connection between Yang-Mills theory and general relativity. Taking known solutions of the Yang-Mills equations (e.g. the topological BPS monopole solutions) it is possible to construct exact solutions to the general relativistic field equations. Although the general relativistic solutions were found starting from known solutions of Yang-Mills theory they have different physical characteristics.