Wormholes and Flux Tubes in the 7D Gravity on the Principal Bundle with SU(2) Gauge Group as the Extra Dimensions

TL;DR

This paper explores vacuum solutions in 7D gravity with SU(2) gauge symmetry, revealing wormhole-like and flux tube configurations, and extends previous U(1) results to a non-Abelian gauge group.

Contribution

It generalizes previous U(1) solutions to SU(2), deriving new spherically symmetric vacuum solutions with off-diagonal metrics in multidimensional gravity.

Findings

Existence of wormhole-like solutions with 4D base

Presence of gravitational flux tubes with color and electric charges

Solution characteristics depend on electric and magnetic field parameters

Abstract

Vacuum solutions for multidimensional gravity on the principal bundle with the SU(2) structural group as the extra dimensions are found and discussed. This generalizes the results of Ref. \cite{vds3} from U(1) to the SU(2) gauge group. The spherically symmetric solution with the off-diagonal components of the multidimensional metric is obtained. It is shown that two types of solutions exist: the first has a wormhole-like 4D base, the second is a gravitational flux tube with two color and electric charges. The solution depends only on two parameters: the values of the electric and magnetic fields at the origin. In the plane of these parameters there exists a curve separating the regions with different types of solutions. An analogy with the 5D solutions is discussed.