Lorentzian manifolds and scalar curvature invariants

Abstract

We discuss (arbitrary-dimensional) Lorentzian manifolds and the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. Recently, we have shown that in four dimensions a Lorentzian spacetime metric is either $\mathcal{I}$-non-degenerate, and hence locally characterized by its scalar polynomial curvature invariants, or is a degenerate Kundt spacetime. We present a number of results that generalize these results to higher dimensions and discuss their consequences and potential physical applications.

submitted to CQG

References in corpus (14)

• Classification of the Weyl Tensor in Higher Dimensions and Applications
• Spacetimes characterized by their scalar curvature invariants
• Kundt Spacetimes
• Robinson-Trautman spacetimes in higher dimensions
• Lorentzian spacetimes with constant curvature invariants in four dimensions
• General Kundt spacetimes in higher dimensions
• Lorentzian spacetimes with constant curvature invariants in three dimensions
• Higher dimensional bivectors and classification of the Weyl operator
• Curvature operators and scalar curvature invariants
• Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity
• Supersymmetry, holonomy and Kundt spacetimes
• Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation
• Type II Einstein spacetimes in higher dimensions
• On Kerr-Schild spacetimes in higher dimensions

Cited by in corpus (16)

• New Exact Solutions of Quadratic Curvature Gravity
• Local Invariants Vanishing on Stationary Horizons: A Diagnostic for Locating Black Holes
• The Curious Case of Null Warped Space
• Local and gauge invariant observables in gravity
• Embedding nonrelativistic physics inside a gravitational wave
• AdS-Wave Solutions of f(Riemann) Theories
• A spacetime not characterised by its invariants is of aligned type II
• Mathematical General Relativity
• Gyratons on Melvin spacetime
• Ultrarelativistic boost of a black hole in the magnetic universe of Levi-Civita--Bertotti--Robinson
• Differential invariants of Kundt spacetimes
• Weyl type N solutions with null electromagnetic fields in the Einstein-Maxwell $p$-form theory
• Lovelock vacua with a recurrent null vector field
• $\mathcal{I}$-Preserving Diffeomorphisms of Lorentzian Manifolds
• On scalar curvature invariants in three dimensional spacetimes
• Nil-Killing vector fields and type III deformations