Gravitational shock waves and scattering amplitudes

Abstract

We study gravitational shock waves using scattering amplitude techniques. After first reviewing the derivation in General Relativity as an ultrarelativistic boost of a Schwarzschild solution, we provide an alternative derivation by exploiting a novel relation between scattering amplitudes and solutions to Einstein's field equations. We prove that gravitational shock waves arise from the classical part of a three point function with two massless scalars and a graviton. The region where radiation is localized has a distributional profile and it is now recovered in a natural way, thus bypassing the introduction of singular coordinate transformations as used in General Relativity. The computation is easily generalized to arbitrary dimensions and we show how the exactness of the classical solution follows from the absence of classical contributions at higher loops. A classical double copy between gravitational and electromagnetic shock waves is also provided and for a spinning source, using the exponential form of three point amplitudes, we infer a remarkable relation between gravitational shock waves and spinning ones, also known as gyratons. Using this property, we infer a family of exact solutions describing gravitational shock waves with spin. We then compute the phase shift of a particle in a background of shock waves finding agreement with an earlier computation by Amati, Ciafaloni and Veneziano for particles in the high energy limit. Applied to a gyraton, it provides a result for the scattering angle to all orders in spin.

23 pages, published on JHEP

References in corpus (15)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Black holes and the double copy
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Tidal Effects in the Post-Minkowskian Expansion
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Classical and quantum double copy of back-reaction
• The double copy for heavy particles
• Kerr-Newman from Minimal Coupling
• Introductory lectures on the Effective One Body formalism
• Strings, extended objects, and the classical double copy
• Electrodynamics of massless charged particles
• Ultrarelativistic boost of the black ring
• Ultrarelativistic boost of spinning and charged black rings

Cited by in corpus (31)

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• The Schwarzschild-Tangherlini metric from scattering amplitudes in various dimensions
• Exponentiation of the leading eikonal with spin
• Celestial holography on Kerr-Schild backgrounds
• New heavenly double copies
• Asymptotic Weyl Double Copy
• Scattering Amplitudes and the Double Copy in Topologically Massive Theories
• Graviton particle statistics and coherent states from classical scattering amplitudes
• Bethe-Salpeter equation for classical gravitational bound states
• Geodesics From Classical Double Copy
• Gravitational Bound Waveforms from Amplitudes
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Classical off-shell currents
• Soft graviton exchange and the information paradox
• From Shockwaves to the Gravitational Memory Effect
• Large Gauge Effects and the Structure of Amplitudes
• Quantization Conditions and the Double Copy
• Wave scattering event shapes at high energies
• Waveforms from Amplitudes
• Rindler Fluids from Gravitational Shockwaves
• The Weyl double copy from twistor space
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction
• Arising of trapped surfaces with non-trivial topology from colliding shock waves
• Classical physics from amplitudes on curved backgrounds
• The Kerr-Schild Double Copy in Lifshitz Spacetime