Global monopole as dual-vacuum solution in Kaluza-Klein spacetime

TL;DR

This paper demonstrates that in Kaluza-Klein spacetime, the global monopole solution is dual to a vacuum solution through a duality transformation that swaps active and passive electric parts of the Riemann curvature, revealing a deep symmetry.

Contribution

It introduces a duality transformation in Kaluza-Klein spacetime that relates global monopole solutions to vacuum solutions, expanding understanding of dualities in higher-dimensional gravity.

Findings

Global monopole solution is dual to vacuum solution in Kaluza-Klein spacetime.

Derived dual solution to flat space representing a massive global monopole.

Identified a massless limit analogous to dual-flat solutions in 4D.

Abstract

By application of the duality transformation, which implies interchange of active and passive electric parts of the Riemann curvature (equivalent to interchange of Ricci and Einstein tensors) it is shown that the global monopole solution in the Kaluza-Klein spacetime is dual to the corresponding vacuum solution. Further we also obtain solution dual to flat space which would in general describe a massive global monopole in 4-dimensional Euclidean space and would have massless limit analogus to the 4-dimensional dual-flat solution.