Vanishing Scalar Invariant Spacetimes in Higher Dimensions
arXiv:gr-qc/0410070 · doi:10.1088/0264-9381/21/23/014
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.
final version
References in corpus (25)
- The Hierarchy Problem and New Dimensions at a Millimeter
- Kaluza-Klein Gravity
- Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
- Penrose limits and maximal supersymmetry
- Exactly solvable model of superstring in Ramond-Ramond plane wave background
- A new maximally supersymmetric background of IIB superstring theory
- Bouncing Braneworlds
- Classification of the Weyl Tensor in Higher Dimensions
- A New Class of Exact Solutions in String Theory
- On solvable models of type IIB superstring in NS-NS and R-R plane wave backgrounds
- All spacetimes with vanishing curvature invariants
- Exact solutions of closed string theory
- Constant magnetic field in closed string theory: an exactly solvable model
- Bianchi identities in higher dimensions
- String vacuum backgrounds with covariantly constant null Killing vector and 2d quantum gravity
- Strings on pp-waves and massive two dimensional field theories
- Generalizations of pp-wave spacetimes in higher dimensions
- General Brane Dynamics with R_{4} term in the Bulk
- A class of exact pp-wave string models with interacting light-cone gauge actions
- Finite sigma models and exact string solutions with Minkowski signature metric
- A Small Note on PP-Wave Vacua in 6 and 5 Dimensions
- Curvature invariants in type N spacetimes
- A Class of Exact Classical Solutions to String Theory
- Null cone preserving maps, causal tensors and algebraic Rainich theory
- Curvature invariants in type-III spacetimes
Cited by in corpus (89)
- Classification of the Weyl Tensor in Higher Dimensions and Applications
- Alignment and algebraically special tensors in Lorentzian geometry
- Spacetimes characterized by their scalar curvature invariants
- On Spacetimes with Constant Scalar Invariants
- Kundt Spacetimes
- Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics
- Algebraic classification of higher dimensional spacetimes based on null alignment
- Generalization of the Geroch-Held-Penrose formalism to higher dimensions
- Ultraspinning instability of rotating black holes
- Lorentzian spacetimes with constant curvature invariants in four dimensions
- Metrics With Vanishing Quantum Corrections
- Ricci identities in higher dimensions
- Higher dimensional VSI spacetimes
- General Kundt spacetimes in higher dimensions
- Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension
- Higher dimensional Kerr-Schild spacetimes
- Lorentzian spacetimes with constant curvature invariants in three dimensions
- Causal structures and causal boundaries
- Gravitational field of relativistic gyratons
- Kerr-Schild spacetimes with (A)dS background
- The Similarity Hypothesis in General Relativity
- WANDs of the Black Ring
- Type III and N universal spacetimes
- Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions
- Higher dimensional bivectors and classification of the Weyl operator
- Symmetry and Equivalence in Teleparallel Gravity
- Interpreting spacetimes of any dimension using geodesic deviation
- Geometric Horizons
- Plane waves in metric-affine gravity
- Embedding nonrelativistic physics inside a gravitational wave
- Identification of black hole horizons using scalar curvature invariants
- AdS-Wave Solutions of f(Riemann) Theories
- Type III and N solutions to quadratic gravity
- Newman-Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction
- Classification of Higher Dimensional Spacetimes
- Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
- Type III and N Einstein spacetimes in higher dimensions: general properties
- The complex Goldberg-Sachs theorem in higher dimensions
- A spacetime not characterised by its invariants is of aligned type II
- Electromagnetic fields with vanishing scalar invariants
- On asymptotically flat algebraically special spacetimes in higher dimensions
- Lorentzian manifolds and scalar curvature invariants
- On higher dimensional Einstein spacetimes with a warped extra dimension
- Static and radiating p-form black holes in the higher dimensional Robinson-Trautman class
- Type II universal spacetimes
- Explicit algebraic classification of Kundt geometries in any dimension
- Charging Kerr-Schild spacetimes in higher dimensions
- Physical interpretation of Kundt spacetimes using geodesic deviation
- Extended Kerr-Schild spacetimes: General properties and some explicit examples
- Pseudo-Riemannian VSI spaces II
- Universal electromagnetic fields
- Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions
- Refinements of the Weyl tensor classification in five dimensions
- Einstein-Maxwell fields as solutions of higher-order theories
- Vanishing Scalar Invariant Spacetimes in Supergravity
- Almost universal spacetimes in higher-order gravity theories
- VSI_i spacetimes and the epsilon-property
- Kerr-Schild double copy for Kundt spacetimes of any dimension
- Asymptotic behaviour of the Weyl tensor in higher dimensions
- On the Goldberg-Sachs theorem in higher dimensions in the non-twisting case
- Kundt spacetimes in the Einstein-Gauss-Bonnet theory
- Pseudo-Riemannian VSI spaces
- Type III Einstein-Yang-Mills solutions
- -degenerate pseudo-Riemannian metrics
- Counting the number of Killing vectors in a 3D spacetime
- Isometries in higher dimensional CCNV spacetimes
- On the uniqueness of the Myers-Perry spacetime as a type II(D) solution in six dimensions
- A criterion for the existence of Killing vectors in 3D
- Nonvanishing Local Scalar Invariants even in VSI Spacetimes with all Polynomial Curvature Scalar Invariants Vanishing
- Hidden symmetries from distortions of the conformal structure
- SO(n + 1) Symmetric Solutions of the Einstein Equations in Higher Dimensions
- Einstein-Maxwell fields with vanishing higher-order corrections
- On the algebraic classification of pseudo-Riemannian spaces
- Weyl type N solutions with null electromagnetic fields in the Einstein-Maxwell -form theory
- Teleparallel geometries not characterized by their scalar polynomial torsion invariants
- -Preserving Diffeomorphisms of Lorentzian Manifolds
- Five dimensional Weyl double copy
- Lovelock vacua with a recurrent null vector field
- Anisotropic Schrödinger black holes with hyperscaling-violation
- The Dynamics of Brane-World Cosmological Models
- Real GIT with applications to compatible representations and Wick-rotations
- Locally Homogeneous Kundt Triples and CSI Metrics
- On the uniqueness of the Kerr-(A)dS metric as a type II(D) solution in six dimensions
- All non-expanding gravitational waves in -dimensional (anti-)de Sitter space
- Exact gyratons in higher and infinite derivative gravity
- Nil-Killing vector fields and type III deformations
- Killing vectors in higher dimensional spacetimes with constant scalar curvature invariants
- A peeling theorem for the Weyl tensor in higher dimensions
- Gauge fields with vanishing scalar invariants