Examples of Einstein spacetimes with recurrent null vector fields

TL;DR

This paper explores Einstein spacetimes with recurrent null vector fields, providing explicit examples and analyzing their geometric properties such as holonomy, Petrov types, and symmetries.

Contribution

It constructs specific examples of Einstein spacetimes with recurrent null vectors and analyzes their holonomy, Petrov classification, and Killing symmetries.

Findings

Explicit examples of Einstein spacetimes with recurrent null vectors

Classification of holonomy algebras for these spacetimes

Determination of Petrov types and Killing vector Lie algebras

Abstract

The Einstein Equation on 4-dimensional Lorentzian manifolds admitting recurrent null vector fields is discussed. Several examples of a special form are constructed. The holonomy algebras, Petrov types and the Lie algebras of Killing vector fields of the obtained metrics are found.