Double Ernst Solution in Einstein-Kalb-Ramond Theory

TL;DR

This paper explores the Kähler formulation of 5D Einstein-Kalb-Ramond theory with two symmetries, establishing solution-generating maps and deriving a class of solutions based on the double Ernst approach, including a double Kerr solution with a horizon.

Contribution

It introduces a Kähler formulation for 5D Einstein-Kalb-Ramond theory with two symmetries and constructs new solutions using double Ernst methods.

Findings

Established three Kramer-Neugebauer-like maps for the 2D case.

Constructed a class of solutions based on the double Ernst approach.

Identified the double Kerr solution as an EKR dipole with a horizon.

Abstract

The K\"ahler formulation of 5-dimensional Einstein-Kalb-Ramond (EKR) theory admitting two commuting Killing vectors is presented. Three different Kramer-Neugebauer-like maps are established for the 2-dimensional case. A class of solutions constructed on the double Ernst one is obtained. It is shown that the double Kerr solution corresponds to a EKR dipole configuration with horizon.