Spinor-helicity and the algebraic classification of higher-dimensional spacetimes

Abstract

The spinor-helicity formalism is an essential technique of the amplitudes community. We draw on this method to construct a scheme for classifying higher-dimensional spacetimes in the style of the four-dimensional Petrov classification and the Newman-Penrose formalism. We focus on the five-dimensional case for concreteness. Our spinorial scheme naturally reproduces the full structure previously seen in both the CMPP and de Smet classifications, and resolves longstanding questions concerning the relationship between the two classifications.

arXiv comment47 pages, 3 figures, 15 tables. v2: minor changes

References in corpus (56)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Black Holes in Higher Dimensions
• Black holes and the double copy
• The Kinematic Algebra From the Self-Dual Sector
• Radiation and the classical double copy for color charges
• The classical double copy for Taub-NUT spacetime
• Classification of the Weyl Tensor in Higher Dimensions
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Amplitudes and Spinor-Helicity in Six Dimensions
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• The Kerr-Schild double copy in curved spacetime
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Yang-Mills origin of gravitational symmetries
• Scattering on plane waves and the double copy
• Gravitational Radiation from Color-Kinematics Duality
• Spinning particles, axion radiation, and the classical double copy
• Bound states and the classical double copy
• Alignment and algebraically special tensors in Lorentzian geometry
• Vanishing Scalar Invariant Spacetimes in Higher Dimensions
• Relationship Between Gravity and Gauge Scattering in the High Energy Limit
• Scattering Amplitudes
• Gravity as Gauge Theory Squared: A Ghost Story
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy
• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• New Horizons for Black Holes and Branes
• Type D Einstein spacetimes in higher dimensions
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• Screw-symmetric gravitational waves: a double copy of the vortex
• Black holes on cylinders are not algebraically special
• Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes
• Simple superamplitudes in higher dimensions
• Gravitational radiation from the classical spinning double copy
• WANDs of the Black Ring
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• Higher dimensional bivectors and classification of the Weyl operator
• Peeling of the Weyl tensor and gravitational radiation in higher dimensions
• On a five-dimensional version of the Goldberg-Sachs theorem
• Geometric Horizons
• Identification of black hole horizons using scalar curvature invariants
• Perturbations of higher-dimensional spacetimes
• Newman-Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction
• Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation
• Spinor classification of the Weyl tensor in five dimensions
• The complex Goldberg-Sachs theorem in higher dimensions
• The perturbation theory of higher dimensional spacetimes a la Teukolsky
• Three-dimensional spacetimes of maximal order
• Spacetime invariants and their uses
• The Cartan Algorithm in Five Dimensions
• Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions
• Refinements of the Weyl tensor classification in five dimensions
• Cartan Invariants and Event Horizon Detection, Extended Version

Cited by in corpus (18)

• The self-dual classical double copy, and the Eguchi-Hanson instanton
• A Twistorial Foundation for the Classical Double Copy
• S-duality and the Double Copy
• Topology and Wilson lines: global aspects of the double copy
• The Classical Double Copy of a Point Charge
• The convolutional double copy: a case study with a point
• Weyl doubling
• Monopoles, shockwaves and the classical double copy
• Biadjoint wires
• New heavenly double copies
• Scattering Amplitudes and the Double Copy in Topologically Massive Theories
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Kerr-Schild double copy for Kundt spacetimes of any dimension
• Weyl double copy in type D spacetime in four and five dimensions
• The Weyl double copy from twistor space
• Five dimensional Weyl double copy
• The Kerr-Schild Double Copy in Lifshitz Spacetime
• NS-NS Spacetimes from Amplitudes