Classical Solutions and their Double Copy in Split Signature

Abstract

The three-point amplitude is the key building block in the on-shell approach to scattering amplitudes. We show that the classical objects computed by massive three-point amplitudes in gauge theory and gravity are Newman-Penrose scalars in a split-signature spacetime, where three-point amplitudes can be defined for real kinematics. In fact, the quantum state set up by the particle is a coherent state fully determined by the three-point amplitude due to an eikonal-type exponentiation. Having identified this simplest classical solution from the perspective of scattering amplitudes, we explore the double copy of the Newman-Penrose scalars induced by the traditional double copy of amplitudes, and find that it coincides with the Weyl version of the classical double copy. We also exploit the Kerr-Schild version of the classical double copy to determine the exact spacetime metric in the gravitational case. Finally, we discuss the direct implication of these results for Lorentzian signature via analytic continuation.

arXiv comment45 pages, 5 figures

References in corpus (119)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• General relativity as an effective field theory: The leading quantum corrections
• New Relations for Gauge-Theory Amplitudes
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Leading Quantum Correction to the Newtonian Potential
• 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
• Black holes and the double copy
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• High-energy gravitational scattering and the general relativistic two-body problem
• General Relativity from Scattering Amplitudes
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Classical Space-Times from the S Matrix
• 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
• Classical black hole scattering from a worldline quantum field theory
• From Boundary Data to Bound States
• Eikonal Quantum Gravity and Planckian Scattering
• Observables and amplitudes for spinning particles and black holes
• The simplest massive S-matrix: from minimal coupling to Black Holes
• Black-hole scattering with general spin directions from minimal-coupling amplitudes
• On-shell Techniques and Universal Results in Quantum Gravity
• Kerr Black Holes as Elementary Particles
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• On Post-Minkowskian Hamiltonians in General Relativity
• On-shell heavy particle effective theories
• From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Universality of ultra-relativistic gravitational scattering
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• Bending of Light in Quantum Gravity
• Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions
• Heavy Black Hole Effective Theory
• Yang-Mills origin of gravitational symmetries
• Scattering on plane waves and the double copy
• Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order
• Type D Spacetimes and the Weyl Double Copy
• Light-like Scattering in Quantum Gravity
• Universality in the classical limit of massless gravitational scattering
• Tidal Effects in the Post-Minkowskian Expansion
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• Post-Minkowskian Scattering Angle in Einstein Gravity
• Relationship Between Gravity and Gauge Scattering in the High Energy Limit
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• Second-order Post-Minkowskian scattering in arbitrary dimensions
• Gravity as Gauge Theory Squared: A Ghost Story
• A Twistorial Foundation for the Classical Double Copy
• The Double Copy of Electric-Magnetic Duality
• Logarithmic Terms in the Soft Expansion in Four Dimensions
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• A worldsheet for Kerr
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Kerr-Schild Double Field Theory and Classical Double Copy
• Next-to-soft corrections to high energy scattering in QCD and gravity
• S-duality and the Double Copy
• The Weyl Double Copy for Gravitational Waves
• Observational Signature of the Logarithmic Terms in the Soft Graviton Theorem
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level
• Screw-symmetric gravitational waves: a double copy of the vortex
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• Tidal effects in quantum field theory
• Topology and Wilson lines: global aspects of the double copy
• Kleinian Geometry and the N=2 Superstring
• Wilson line approach to gravity in the high energy limit
• The classical double copy of non-singular black holes
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Mining the Geodesic Equation for Scattering Data
• The Classical Double Copy of a Point Charge
• 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
• Gravity Waves from Soft Theorem in General Dimensions
• On higher-derivative effects on the gravitational potential and particle bending
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Ehlers as EM duality in the double copy
• The double copy for heavy particles
• Classical and quantum double copy of back-reaction
• The Newman-Penrose Map and the Classical Double Copy
• Weyl doubling
• Kerr-Schild Double Copy and Complex Worldlines
• Monopoles, shockwaves and the classical double copy
• The Schwarzschild-Tangherlini metric from scattering amplitudes in various dimensions
• Classical Sub-subleading Soft Photon and Soft Graviton Theorems in Four Spacetime Dimensions
• High-energy string-brane scattering: leading eikonal and beyond
• Gravitational shock waves and scattering amplitudes
• Strings, extended objects, and the classical double copy
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• The Subleading Eikonal in Supergravity Theories
• New heavenly double copies
• A Classical Proof of the Classical Soft Graviton Theorem in D>4
• Loop-Level Double-Copy for Massive Quantum Particles
• Scattering Amplitudes and the Double Copy in Topologically Massive Theories
• A note on the absence of $R^2$ corrections to Newton's potential
• Asymptotic dynamics on the worldline for spinning particles
• On the Lagrangian formulation of the double copy to cubic order
• Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor
• Soft Radiation from Scattering Amplitudes Revisited
• Gauge $\times$ Gauge on Spheres
• Light-ray operators, detectors and gravitational event shapes
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• $\mathcal{N}=1$ Supersymmetric Double Field Theory and the generalized Kerr-Schild Ansatz
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• From polarized gravitational waves to analytically solvable electromagnetic beams
• Gravitational Dyonic Amplitude at One-Loop and its Inconsistency with the Classical Impulse
• Taub-NUT from the Dirac monopole
• Perturbation theory in (2,2) signature

Cited by in corpus (43)

• Classical observables from coherent-spin amplitudes
• Covariant Color-Kinematics Duality
• Sources in the Weyl double copy
• Classical double copy at null infinity
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Classical Double Copy of Worldline Quantum Field Theory
• Celestial holography on Kerr-Schild backgrounds
• Double Field Theory as the Double Copy of Yang-Mills
• Asymptotic Weyl Double Copy
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Twistor Space Origins of the Newman-Penrose Map
• Black Holes in Klein Space
• The double copy of the multipole expansion
• Graviton particle statistics and coherent states from classical scattering amplitudes
• Bethe-Salpeter equation for classical gravitational bound states
• Why is the Weyl double copy local in position space?
• Geodesics From Classical Double Copy
• Non-perturbative aspects of the self-dual double copy
• Higher-derivative Heterotic Double Field Theory and Classical Double Copy
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Gravitational Bound Waveforms from Amplitudes
• Classical Double Copy of Spinning Worldline Quantum Field Theory
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• Large Gauge Effects and the Structure of Amplitudes
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• Note on the asymptotic structure of Kerr-Schild form
• Wave scattering event shapes at high energies
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Asymptotic Weyl double copy in Newman-Penrose formalism
• Waveforms from Amplitudes
• Compactifying the Kerr-Schild Double Copy
• Next-to-MHV Yang-Mills kinematic algebra
• Weyl double copy in type D spacetime in four and five dimensions
• Five dimensional Weyl double copy
• New framework for classical double copies
• A functional approach to the next to eikonal approximation of high energy gravitational scattering
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction
• From colored gravity to electromagnetism
• Classical physics from amplitudes on curved backgrounds
• The Radial Action from Probe Amplitudes to All Orders
• Quantum field theory in flat spacetime with multiple time directions
• NS-NS Spacetimes from Amplitudes