Nil-Killing vector fields and type III deformations

TL;DR

This paper investigates deformations of Kundt metrics via nil-Killing vector fields, providing classifications and criteria for preserving scalar polynomial invariants and characterizing Kundt-CSI spacetimes.

Contribution

It introduces new characterizations of Kundt metrics using nil-Killing vector fields and classifies algebraic stability of tensors under type III deformations.

Findings

Characterization of Kundt metrics in terms of nil-Killing vector fields

Criteria for preserving scalar polynomial invariants under deformations

Lie algebra structures of nil-Killing vector fields for degenerate Kundt metrics

Abstract

This paper is concerned with deformations of Kundt metrics in the direction of type $III$ tensors and nil-Killing vector fields whose flows give rise to such deformations. We find various characterizations within the Kundt class in terms of nil-Killing vector fields and obtain a theorem classifying algebraic stability of tensors, which has an application in finding sufficient criteria for a type $III$ deformation of the metric to preserve spi's. This is used in order to specify Lie algebras of nil-Killing vector fields that preserve the spi's, for degenerate Kundt metrics. Using this we discuss the characterization of Kundt-CSI spacetimes in terms of nil-Killing vector fields.