Generalized Ernst Potentials for arbitrary Dilatonic Theories

TL;DR

This paper extends Ernst potentials to Einstein-Maxwell-Dilaton theories, providing a new formalism that simplifies the analysis and discovery of exact solutions in these complex spacetimes.

Contribution

It generalizes Ernst potentials and potential space metrics to the dilatonic case, enabling easier analysis and solution generation in Einstein-Maxwell-Dilaton theories.

Findings

Derived the generalized Ernst potentials for dilatonic theories.

Explicitly formulated the potential space metric in five dimensions.

Demonstrated the method's effectiveness by recovering and discovering solutions.

Abstract

In this work, we generalize Ernst potentials to the Einstein-Maxwell-Dilaton case and explicitly write the corresponding potential space metric. Since this metric is five-dimensional in potential space, we generalize the corresponding Newman-Penrose coefficients for this metric and compare this formalism with previous approaches to show that this formulation is very convenient for analyzing these spacetimes and finding new exact solutions. We show how to obtain old exact solutions and some new ones with very interesting properties.