On the invariant symmetries of the $\mathcal{D}$-metrics

TL;DR

This paper investigates the symmetries and invariant properties of a specific class of Einstein-Maxwell solutions, revealing new insights into their isometry groups and characterizing features of the Kerr-NUT subfamily.

Contribution

It identifies new invariant qualities of $ ext{D}$-metrics and characterizes when these symmetries define the metric family, including the Kerr-NUT solutions.

Findings

Determined properties of the isometry group of $ ext{D}$-metrics.

Identified conditions under which invariant symmetries characterize the metric family.

Showed Kerr-NUT solutions admit a Papapetrou field aligned with the Weyl tensor.

Abstract

We analyze the symmetries and other invariant qualities of the $\mathcal{D}$-metrics (type D aligned Einstein Maxwell solutions with cosmological constant whose Debever null principal directions determine shear-free geodesic null congruences). We recover some properties and deduce new ones about their isometry group and about their quadratic first integrals of the geodesic equation, and we analyze when these invariant symmetries characterize the family of metrics. We show that the subfamily of the Kerr-NUT solutions are those admitting a Papapetrou field aligned with the Weyl tensor.