Symmetries of the dual metrics

TL;DR

This paper investigates the symmetries of dual manifolds, identifying conditions under which a manifold and its dual share symmetries, with detailed analysis of Einstein metrics, Kerr-Newman geometry, and separable coordinates.

Contribution

It derives conditions for dual manifolds to have identical symmetries and analyzes specific examples like Kerr-Newman geometry and separable coordinates.

Findings

Conditions for shared Killing vectors and Killing-Yano tensors

Equations for dual metrics of Einstein spaces

Detailed analysis of Kerr-Newman and separable coordinates

Abstract

In this paper the symmetries of the dual manifold were investigated. We found the conditions when the manifold and its dual admit the same Killing vectors and Killing-Yano tensors. In the case of an Einstein's metric $g_{\mu\nu}$ the corresponding equations for its dual were found. The examples of Kerr-Newman geometry and the separable coordinates in 1+1 dimensions were analyzed in details.