Petrov type I spacetime curvature: principal null vector spanning dimension

TL;DR

This paper classifies Petrov type I spacetimes based on the dimensional span of their principal null directions, providing explicit examples for both vacuum and nonvacuum cases.

Contribution

It introduces a new classification of Petrov type I spacetimes by the span dimension of principal null directions and supplies explicit examples for each category.

Findings

Maximally spanning type I spacetimes have four principal null directions.

Nonmaximally spanning type I spacetimes have three principal null directions.

Explicit examples are provided for vacuum and nonvacuum spacetimes.

Abstract

The class of Petrov type I curvature tensors is further divided into those for which the span of the set of distinct principal null directions has dimension four (maximally spanning type I) or dimension three (nonmaximally spanning type I). Explicit examples are provided for both vacuum and nonvacuum spacetimes.