Ehlers--Harrison--Type Transformations in Dilaton--Axion Gravity

TL;DR

The paper demonstrates that four‑dimensional Einstein–Maxwell–Dilaton–Axion gravity with a Killing vector admits a ten‑parameter internal symmetry that unifies dilaton–axion SL(2,R) duality with Harrison– and Ehlers–type transformations via a three‑dimensional sigma‑model reduction. This symmetry provides a systematic method to generate axidilaton counterparts to vacuum and EMDA solutions, culminating in a seven‑parameter rotating Kerr–NUT dyon with dilaton and axion fields. The construction recovers known solutions in special limits (eg Sen, Kallosh–Ortín) and reveals rich structure in extremal and Taub–NUT regimes, including thermodynamic properties. The results also point toward possible integrability for multi‑ Killing configurations and a deeper link to established groups like Kinnersley and Geroch in reduced gravity theories.

Abstract

The ten--parametric internal symmetry group is found in the $D=4$ Einstein--Maxwell--Dilaton--Axion theory restricted to space--times admitting a Killing vector field. The group includes dilaton--axion $SL(2,R)$ duality and Harrison--type transformations which are similar to some target--space duality boosts, but act on a different set of variables. New symmetry is used to derive a seven--parametric family of rotating dilaton--axion Taub--NUT dyons.