Hidden Simplicity of the Gravity Action

Abstract

We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons and a single auxiliary field. The corresponding equations of motion are the Einstein field equations rewritten as two coupled first-order differential equations. Since all Feynman diagrams are cubic, we are able to derive new off-shell recursion relations for tree-level graviton scattering amplitudes. With a judicious choice of gauge fixing, we then construct an especially compact form for the Einstein-Hilbert action in which all graviton interactions are simply proportional to the graviton kinetic term. Our results apply to graviton perturbations about an arbitrary curved background spacetime.

20 pages, 1 figure

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• GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
• New Relations for Gauge-Theory Amplitudes
• Black holes and the double copy
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Symmetry and Action for Flavor-Kinematics Duality
• Twofold Symmetries of the Pure Gravity Action
• Three Applications of a Bonus Relation for Gravity Amplitudes

Cited by in corpus (37)

• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• The Kerr-Schild double copy in curved spacetime
• Double copy for massive quantum particles with spin
• Gravitational Radiation from Color-Kinematics Duality
• Type D Spacetimes and the Weyl Double Copy
• Tidal Effects in the Post-Minkowskian Expansion
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• Kerr-Schild Double Field Theory and Classical Double Copy
• Double Copy from Homotopy Algebras
• Double Copy for Celestial Amplitudes
• Covariant Color-Kinematics Duality
• Gravitational radiation from the classical spinning double copy
• The Newman-Penrose Map and the Classical Double Copy
• Double Field Theory as the Double Copy of Yang-Mills
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• The Two-Loop Four-Graviton Scattering Amplitudes
• Twistor Space Origins of the Newman-Penrose Map
• On the Lagrangian formulation of the double copy to cubic order
• Graviton particle statistics and coherent states from classical scattering amplitudes
• Towards Color-Kinematics Duality in Generic Spacetimes
• Gauge $\times$ Gauge on Spheres
• Non-perturbative aspects of the self-dual double copy
• Gravity-Matter Feynman Rules for any Valence
• Multiparticle solutions to Einstein's equations
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• Double copy for Lagrangians at trilinear order
• Beyond the standard model with six-dimensional spinors
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• On the `simple' form of the gravitational action and the self-interacting graviton
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering
• Higher curvature gravities, unlike GR, cannot be bootstrapped from their (usual) linearizations
• Perturbations of General Relativity to All Orders and the General $n^{\mathrm{th}}$ Order Terms
• Chiral perturbation theory for GR
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction
• Quantum Off-Shell Recursion Relation
• FeynGrav 4.0