Vanishing scalar invariant spacetimes in higher dimensions

2004/10/31 by A. Coley, A Coley, R. Milson +5 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/21/23/014

published as Class.Quant.Grav.21:5519-5542,2004 · final version

arxiv created 2004/11/17 · openalex publication_date 2004/11/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study manifolds with Lorentzian signature and prove that all scalar curvature invariants of all orders vanish in a higher-dimensional Lorentzian spacetime if and only if there exists an aligned non-expanding, non-twisting, geodesic null direction along which the Riemann tensor has negative boost order.

Citations

• A Class of Exact Classical Solutions to String Theory
• Spacetime singularities in string theory
• Curvature invariants in type-III spacetimes

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• On higher dimensional Einstein spacetimes with a warped extra dimension
• Asymptotically flat, algebraically special spacetimes in higher dimensions
• Higher dimensional Kerr–Schild spacetimes