Kerr-Schild Structure and Harmonic 2-forms on (A)dS-Kerr-NUT Metrics

TL;DR

This paper reveals that (A)dS-Kerr-NUT solutions in higher dimensions can be expressed in a multi-Kerr-Schild form with linear parameters, and constructs harmonic 2-forms linked to charged solutions and Calabi-Yau metrics.

Contribution

It demonstrates the Kerr-Schild structure of (A)dS-Kerr-NUT metrics and constructs harmonic 2-forms, connecting solutions to charged and Calabi-Yau geometries.

Findings

Metrics admit mutually-orthogonal null geodesic congruences.

Metrics can be written in multi-Kerr-Schild form with linear parameters.

Constructed harmonic 2-forms related to charged solutions and Calabi-Yau limits.

Abstract

We demonstrate that the general (A)dS-Kerr-NUT solutions in D dimensions with ([D/2], [(D+1)/2]) signature admit [D/2] linearly-independent, mutually-orthogonal and affinely-parameterised null geodesic congruences. This enables us to write the metrics in a multi-Kerr-Schild form, where the mass and all of the NUT parameters enter the metrics linearly. In the case of D=2n, we also obtain n harmonic 2-forms, which can be viewed as charged (A)dS-Kerr-NUT solution at the linear level of small-charge expansion, for the higher-dimensional Einstein-Maxwell theories. In the BPS limit, these 2-forms reduce to n-1 linearly-independent ones, whilst the resulting Calabi-Yau metric acquires a Kahler 2-form, leaving the total number the same.