Petrov type I spacetime curvature: principal null vector spanning dimension

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.

v1: 16 pages; v2: 21 pages, references added, discussion expanded; v3: 21 pages, final version matching the published one

References in corpus (1)

• Investigating new forms of gravity-matter couplings in the gravitational field equations

Cited by in corpus (3)

• Visualization and analysis of the curvature invariants in the Alcubierre warp-drive spacetime
• A Closer Look at Natário's Zero-Expansion Warp Drive
• Wedging spacetime principal null directions