Isometries and the double copy

Abstract

In the standard derivation of the Kerr-Schild double copy, the geodicity of the Kerr-Schild vector and the stationarity of the spacetime are presented as assumptions that are necessary for the single copy to satisfy Maxwell's equations. However, it is well known that the vacuum Einstein equations imply that the Kerr-Schild vector is geodesic and shear-free, and that the spacetime possesses a distinguished vector field that is simultaneously a Killing vector of the full spacetime and the flat background, but need not be timelike with respect to the background metric. We show that the gauge field obtained by contracting this distinguished Killing vector with the Kerr-Schild graviton solves the vacuum Maxwell equations, and that this definition of the Kerr-Schild double copy implies the Weyl double copy when the spacetime is Petrov type D. When the Killing vector is taken to be timelike with respect to the background metric, we recover the familiar Kerr-Schild double copy, but the prescription is well defined for any vacuum Kerr-Schild spacetime and we present new examples where the Killing vector is null or spacelike. While most examples of physical interest are type D, vacuum Kerr-Schild spacetimes are generically of Petrov type II. We present a straightforward example of such a spacetime and study its double copy structure. Our results apply to real Lorentzian spacetimes as well as complex spacetimes and real spacetimes with Kleinian signature, and provide a simple correspondence between real and self-dual vacuum Kerr-Schild spacetimes. This correspondence allows us to study the double copy structure of a self-dual analog of the Kerr spacetime. We provide evidence that this spacetime may be diffeomorphic to the self-dual Taub-NUT solution.

Typographical errors corrected, results unchanged

References in corpus (61)

• New Relations for Gauge-Theory Amplitudes
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Gravity as the Square of Gauge Theory
• Black holes and the double copy
• Radiation and the classical double copy for color charges
• The classical double copy for Taub-NUT spacetime
• From Boundary Data to Bound States
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Kerr Black Holes as Elementary Particles
• The double copy: Bremsstrahlung and accelerating black holes
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Scattering on plane waves and the double copy
• Gravitational Radiation from Color-Kinematics Duality
• Type D Spacetimes and the Weyl Double Copy
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Bound states and the classical double copy
• A Twistorial Foundation for the Classical Double Copy
• The Double Copy of Electric-Magnetic Duality
• Exact solutions for the biadjoint scalar field
• Kerr-Schild Double Field Theory and Classical Double Copy
• Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions
• S-duality and the Double Copy
• The Weyl Double Copy for Gravitational Waves
• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
• Screw-symmetric gravitational waves: a double copy of the vortex
• The classical double copy of non-singular black holes
• The Classical Double Copy of a Point Charge
• The convolutional double copy: a case study with a point
• Extended solutions for the biadjoint scalar field
• Classical Yang-Mills observables from amplitudes
• A double copy for asymptotic symmetries in the self-dual sector
• Twofold Symmetries of the Pure Gravity Action
• Ehlers as EM duality in the double copy
• The Newman-Penrose Map and the Classical Double Copy
• Kerr-Schild Double Copy and Complex Worldlines
• Classical double copy at null infinity
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Biadjoint wires
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• Classical Double Copy: Kerr-Schild-Kundt metrics from Yang-Mills Theory
• New heavenly double copies
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• 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
• The double copy of the multipole expansion
• Non-perturbative aspects of the self-dual double copy
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Weyl double copy and massless free fields in curved spacetimes
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• Classical double copy and higher-spin fields

Cited by in corpus (14)

• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Kerr-Schild double copy for Kundt spacetimes of any dimension
• Asymptotic Weyl double copy in Newman-Penrose formalism
• 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
• Five dimensional Weyl double copy
• New framework for classical double copies
• A note on the area of event horizon of Kleinian black hole
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction
• Untwisting the double copy: the zeroth copy as an optical seed
• Residual Symmetries and Their Algebras in the Kerr-Schild Double Copy
• Newman-Janis Algorithm from Taub-NUT Instantons