Kundt Structures

TL;DR

This paper introduces a novel approach to studying Kundt spacetimes using $G$-structures, defining a Lie-group framework that characterizes these spacetimes through integrability and automorphism properties.

Contribution

It develops a new $G$-structure-based method to analyze Kundt spacetimes, including conditions for integrability and automorphisms, and characterizes invariant structures on homogeneous manifolds.

Findings

Defined a Lie-group $GN$ for Kundt structures.

Established that automorphisms form a nil-Killing vector field algebra.

Characterized all invariant Kundt structures on homogeneous manifolds.

Abstract

In this paper we consider a new approach to studying Kundt spacetimes through $G$-structures. We define a Lie-group $GN$ such that the $GN$-structures satisfying an integrability condition and an existence criterion, which we call Kundt structures, have the property that each metric belonging to the Kundt structure is automatically a Kundt spacetime. We find that the Lie algebra of infinitesimal automorphisms of such structures is given by a Lie algebra of nil-Killing vector fields. Lastly we characterize all left invariant Kundt structures on homogeneous manifolds.