Geroch--Kinnersley--Chitre group for Dilaton--Axion Gravity

TL;DR

This paper develops a new matrix-based representation for the Einstein-Maxwell-dilaton-axion system with two symmetries, simplifying the construction of the Geroch group by relating it to vacuum Einstein equations.

Contribution

It introduces a novel $SL(2,R)$ matrix formulation and an infinite hierarchy of potentials for the system, extending known vacuum Einstein techniques.

Findings

New $SL(2,R)$ matrix formulation for the system

Reduction of Geroch group construction to vacuum Einstein problem

Introduction of an infinite hierarchy of potentials

Abstract

Kinnersley--type representation is constructed for the four--dimensional Einstein--Maxwell--dilaton--axion system restricted to space--times possessing two non--null commuting Killing symmetries. New representation essentially uses the matrix--valued $SL(2,R)$ formulation and effectively reduces the construction of the Geroch group to the corresponding problem for the vacuum Einstein equations. An infinite hierarchy of potentials is introduced in terms of $2\times 2$ real symmetric matrices generalizing the scalar hierarchy of Kinnersley--Chitre known for the vacuum Einstein equations.