Spherically Symmetric solutions in Multidimensional Gravity with the SU(2) Gauge Group as the Extra Dimensions

TL;DR

This paper explores spherically symmetric solutions in multidimensional gravity with SU(2) gauge symmetry, revealing wormhole-like and flux tube configurations that could serve as quantum handles in spacetime foam.

Contribution

It provides a numerical analysis of gravitational solutions with SU(2) gauge fields in higher dimensions, highlighting boundary condition effects on solution types.

Findings

Existence of wormhole-like solutions.

Presence of flux tube solutions.

Solution types depend on boundary conditions.

Abstract

The multidimensional gravity on the principal bundle with the SU(2) gauge group is considered. The numerical investigation of the spherically symmetric metrics with the center of symmetry is made. The solution of the gravitational equations depends on the boundary conditions of the ``SU(2) gauge potential'' (off-diagonal metric components) at the symmetry center and on the type of symmetry (symmetrical or antisymmetrical) of these potentials. In the chosen range of the boundary conditions it is shown that there are two types of solutions: wormhole-like and flux tube. The physical application of such kind of solutions as quantum handles in a spacetime foam is discussed.