Higher dimensional VSI spacetimes

Abstract

We present the explicit metric forms for higher dimensional vanishing scalar invariant (VSI) Lorentzian spacetimes. We note that all of the VSI spacetimes belong to the higher dimensional Kundt class. We determine all of the VSI spacetimes which admit a covariantly constant null vector, and we note that in general in higher dimensions these spacetimes are of Ricci type III and Weyl type III. The Ricci type N subclass is related to the chiral null models and includes the relativistic gyratons and the higher dimensional pp-wave spacetimes. The spacetimes under investigation are of particular interest since they are solutions of supergravity or superstring theory.

14 pages, changes in second paragraph of the discussion

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• Embedding nonrelativistic physics inside a gravitational wave
• Type III and N solutions to quadratic gravity
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• Supersymmetry, holonomy and Kundt spacetimes
• Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation
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• Physical interpretation of Kundt spacetimes using geodesic deviation
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• Vanishing Scalar Invariant Spacetimes in Supergravity
• Gyratons in the Robinson-Trautman and Kundt classes
• Almost universal spacetimes in higher-order gravity theories
• Kerr-Schild double copy for Kundt spacetimes of any dimension
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• Pseudo-Riemannian VSI spaces
• Vacuum Kundt Waves
• $\mathcal{I}$-degenerate pseudo-Riemannian metrics
• Isometries in higher dimensional CCNV spacetimes
• Nonvanishing Local Scalar Invariants even in VSI Spacetimes with all Polynomial Curvature Scalar Invariants Vanishing
• Einstein-Maxwell fields with vanishing higher-order corrections
• Exact Solutions of General Relativity and Quadratic Gravity in Arbitrary Dimension
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• Lovelock vacua with a recurrent null vector field
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• Real GIT with applications to compatible representations and Wick-rotations
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• Spacetimes with all scalar curvature invariants in terms of the Cosmological Constant
• Nil-Killing vector fields and type III deformations
• Gauge fields with vanishing scalar invariants
• Einstein-Yang-Mills fields immune to quantum corrections