Type D Spacetimes and the Weyl Double Copy

Abstract

We study the double-copy relation between classical solutions in gauge theory and gravity, focusing on four-dimensional vacuum metrics of algebraic type D, a class that includes several important solutions. We present a double copy of curvatures that applies to all spacetimes of this type -- the Weyl double copy -- relating the curvature of the spacetime to an electromagnetic field strength. We show that the Weyl double copy is consistent with the previously known Kerr-Schild double copy, and in fact resolves certain ambiguities of the latter. The most interesting new example of the classical double copy presented here is that of the C-metric. This well-known solution, which represents a pair of uniformly accelerated black holes, is mapped to the Lienard-Wiechert potential for a pair of uniformly accelerated charges. We also present a new double-copy interpretation of the Eguchi-Hanson instanton.

27 pages, 1 figure. v2: minor changes. v3: minor correction

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• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
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• Gluons and gravitons at one loop from ambitwistor strings
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• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• Killing-Yano tensors and multi-hermitian structures
• Zero mass limit of Kerr spacetime is a wormhole
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Cancelling the U(1) Anomaly in the S-matrix of N=4 Supergravity
• Radiation of scalar modes and the classical double copy
• On tree amplitudes with gluons coupled to gravitons

Cited by in corpus (92)

• Observables and amplitudes for spinning particles and black holes
• Double copy for massive quantum particles with spin
• The Double Copy of Electric-Magnetic Duality
• A Twistorial Foundation for the Classical Double Copy
• S-duality and the Double Copy
• The Weyl Double Copy for Gravitational Waves
• Double Copy from Homotopy Algebras
• Classical Solutions and their Double Copy in Split Signature
• Topology and Wilson lines: global aspects of the double copy
• Double Copy for Celestial Amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• The classical double copy of non-singular black holes
• Shifting Spin on the Celestial Sphere
• The Classical Double Copy of a Point Charge
• Covariant Color-Kinematics Duality
• The convolutional double copy: a case study with a point
• Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO
• Classical Yang-Mills observables from amplitudes
• A double copy for asymptotic symmetries in the self-dual sector
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Weyl doubling
• Kerr-Newman from Minimal Coupling
• On the Double Copy for Spinning Matter
• Sources in the Weyl double copy
• Classical double copy at null infinity
• Monopoles, shockwaves and the classical double copy
• Gravitational shock waves and scattering amplitudes
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• New heavenly double copies
• Asymptotic Weyl Double Copy
• UV considerations on scattering amplitudes in a web of theories
• Loop-Level Double-Copy for Massive Quantum Particles
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• Gauge invariant double copy of Yang-Mills theory: the quartic theory
• Einstein-Maxwell theory and the Weyl double copy
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Alternative formulations of the twistor double copy
• Twistor Space Origins of the Newman-Penrose Map
• On the Lagrangian formulation of the double copy to cubic order
• Amplitudes, Hopf algebras and the colour-kinematics duality
• The double copy of the multipole expansion
• Black Holes in Klein Space
• Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor
• Why is the Weyl double copy local in position space?
• Gauge $\times$ Gauge on Spheres
• Non-perturbative aspects of the self-dual double copy
• Geodesics From Classical Double Copy
• Isometries and the double copy
• Shift symmetries, soft limits, and the double copy beyond leading order
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• The Weyl double copy in vacuum spacetimes with a cosmological constant
• Classical Double Copy of Spinning Worldline Quantum Field Theory
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Weyl double copy and massless free fields in curved spacetimes
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• From polarized gravitational waves to analytically solvable electromagnetic beams
• Black Hole Horizons from the Double Copy
• Extracting Einstein from the Loop-Level Double-Copy
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Planar solutions of higher-spin theory. Nonlinear corrections
• Regularized Weyl double copy
• Classical double copy and higher-spin fields
• Note on the asymptotic structure of Kerr-Schild form
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• BRST Symmetry and the Convolutional Double Copy
• Kerr-Schild double copy for Kundt spacetimes of any dimension
• Asymptotic Weyl double copy in Newman-Penrose formalism
• The double copy: from optics to quantum gravity
• Waveforms from Amplitudes
• Compactifying the Kerr-Schild Double Copy
• Kaehler geometry of black holes and gravitational instantons
• Gravito-electromagnetism, Kerr-Schild and Weyl double copies; a unified perspective
• Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy
• Weyl double copy in type D spacetime in four and five dimensions
• Background ambiguity and the Gödel double copy
• New framework for classical double copies
• Five dimensional Weyl double copy
• The Weyl double copy from twistor space
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction
• Self-dual gravity via Hitchin's equations
• All non-expanding gravitational waves in $D$-dimensional (anti-)de Sitter space
• Untwisting the double copy: the zeroth copy as an optical seed
• Yang-Mills observables: from KMOC to eikonal through EFT
• Kerr-Schild Double Copy of the Randall-Sundrum Black String
• NS-NS Spacetimes from Amplitudes
• Weyl double copy in Lifshitz spacetimes
• The Kerr-Schild Double Copy in Lifshitz Spacetime
• Cotton Double Copy for Gravitational Waves