Conformally flat Kaluza-Klein spaces, pseudo-/para-complex space forms and generalized gravitational kinks

TL;DR

This paper investigates the equations of conformally flat Kaluza-Klein spaces, classifies solutions with pseudo-Kahler and para-Kahler structures, and identifies gravitational kinks and their deformations across various dimensions and signatures.

Contribution

It introduces a classification of solutions to Kaluza-Klein equations with special geometric structures, including novel gravitational kink solutions.

Findings

Rank two solutions include gravitational kinks and deformations.

Solutions are classified by dimension, signature, and gauge field rank.

New classes of solutions related to pseudo- and para-Kahler structures.

Abstract

The equations describing the Kaluza-Klein reduction of conformally flat spaces are investigated in arbitrary dimensions. Special classes of solution related to pseudo-Kahler and para-Kahler structures are constructed and classified according to spacetime dimension, signature and gauge field rank. Remarkably, rank two solutions include gravitational kinks together with their centripetal and centrifugal deformations.