General Kundt spacetimes in higher dimensions

Abstract

We investigate a general metric of the Kundt class of spacetimes in higher dimensions. Geometrically, it admits a non-twisting, non-shearing and non-expanding geodesic null congruence. We calculate all components of the curvature and Ricci tensors, without assuming any specific matter content, and discuss algebraic types and main geometric constraints imposed by general Einstein's field equations. We explicitly derive Einstein-Maxwell equations, including an arbitrary cosmological constant, in the case of vacuum or possibly an aligned electromagnetic field. Finally, we introduce canonical subclasses of the Kundt family and we identify the most important special cases, namely generalised pp-waves, VSI or CSI spacetimes, and gyratons.

15 pages

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Cited by in corpus (52)

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• Kundt spacetimes as solutions of topologically massive gravity
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• Higher dimensional bivectors and classification of the Weyl operator
• Exact solutions to quadratic gravity
• Interpreting spacetimes of any dimension using geodesic deviation
• Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity
• Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation
• Higher-dimensional Kundt waves and gyratons
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• Electromagnetic fields with vanishing scalar invariants
• Lorentzian manifolds and scalar curvature invariants
• Exact Parallel Waves in General Relativity
• All solutions of Einstein-Maxwell equations with a cosmological constant in 2+1 dimensions
• Gyratons in the Robinson-Trautman and Kundt classes
• Kundt solutions of Minimal Massive 3D Gravity
• Kundt spacetimes in the Einstein-Gauss-Bonnet theory
• Kundt spacetimes minimally coupled to scalar field
• Kerr-Schild double copy for Kundt spacetimes of any dimension
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• Penrose junction conditions extended: impulsive waves with gyratons
• Twisting algebraically special solutions in five dimensions
• Siklos waves with torsion in 3D
• Absence of gyratons in the Robinson-Trautman class
• New metric-affine generalizations of gravitational wave geometries
• Review of gravitational wave solutions in quadratic metric-affine gravity
• The Petrov type D equation on genus $>0$ sections of isolated horizons
• On supersymmetric Einstein-Weyl spaces
• Exact Solutions of General Relativity and Quadratic Gravity in Arbitrary Dimension
• Chaos in Kundt type III Spacetimes
• Type II Einstein spacetimes in higher dimensions
• Near Horizon Geometries and Black Hole Holograph
• Weyl type N solutions with null electromagnetic fields in the Einstein-Maxwell $p$-form theory
• Strings vs Spins on the Null Orbifold
• On conformally recurrent manifolds of dimension greater than 4
• Doubly Torqued Vectors and a classification of Doubly Twisted and Kundt spacetimes
• Almost Robinson geometries
• Classification of Robinson-Trautmann and Kundt Geometries with Large D Limit
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• All non-expanding gravitational waves in $D$-dimensional (anti-)de Sitter space
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• Universal Walker metrics
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• Uniqueness of the Kerr-de Sitter spacetime as an algebraically special solution in five dimensions
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• Killing Spinors -- Beyond Supergravity
• Vacuum Einstein field equations in smooth metric measure spaces: the isotropic case
• Simple conformally recurrent space-times are conformally recurrent PP-waves