Kaluza-Klein reduction of conformally flat spaces

TL;DR

This paper explores the Kaluza-Klein reduction of conformally flat spaces across various dimensions, highlighting elegant equations in three-dimensional reduction and deriving explicit solutions under circular symmetry linked to two-dimensional dilaton gravity.

Contribution

It provides a comprehensive analysis of Kaluza-Klein reduction for conformally flat spaces and connects explicit solutions to dilaton gravity actions.

Findings

Elegant equations for 4-to-3 dimensional reduction

Explicit solutions under circular symmetry

Connection to two-dimensional dilaton gravity

Abstract

Kaluza-Klein reduction of conformally flat spaces is considered for arbitrary dimensions. The corresponding equations are particularly elegant for the reduction from four to three dimensions. Assuming circular symmetry leads to explicit solutions which also arise from specific two-dimensional dilaton gravity actions.