Centrifugal deformations of the gravitational kink

TL;DR

This paper revisits the Kaluza-Klein reduction of 4d conformally flat spacetimes, revealing that the resulting 3d equations relate to 2d gravitational kink equations with a centrifugal term, leading to disconnected spacetime regions.

Contribution

It demonstrates the equivalence between 3d reduced equations and 2d gravitational kink equations with centrifugal effects, providing new insights into spacetime structure.

Findings

Space-like gauge fields induce disconnected spacetime regions.

Centrifugal terms modify gravitational kink solutions.

Reinterpretation of 4d conformally flat spacetimes in lower dimensions.

Abstract

The Kaluza-Klein reduction of 4d conformally flat spacetimes is reconsidered. The corresponding 3d equations are shown to be equivalent to 2d gravitational kink equations augmented by a centrifugal term. For space-like gauge fields and non-trivial values of the centrifugal term the gravitational kink solutions describe a spacetime that is divided in two disconnected regions.