Einstein--Maxwell--Dilaton metrics from three--dimensional Einstein--Weyl structures

TL;DR

This paper constructs time-dependent Einstein-Maxwell-dilaton solutions in four dimensions using three-dimensional Einstein-Weyl structures linked to integrable systems, derived via Kaluza-Klein reduction of higher-dimensional solitons.

Contribution

It introduces a novel method to generate Einstein-Maxwell-dilaton metrics from Einstein-Weyl geometries related to integrable equations.

Findings

Derived explicit time-dependent solutions with attractive electric force.

Connected Einstein-Weyl structures to integrable PDEs like KP and Toda.

Implemented Kaluza-Klein reduction from higher-dimensional solitons.

Abstract

A class of time dependent solutions to $(3+1)$ Einstein--Maxwell-dilaton theory with attractive electric force is found from Einstein--Weyl structures in (2+1) dimensions corresponding to dispersionless Kadomtsev--Petviashvili and $SU(\infty)$ Toda equations. These solutions are obtained from time--like Kaluza--Klein reductions of $(3+2)$ solitons.