Classical Gravity from Loop Amplitudes

Abstract

We describe an efficient method for extracting the parts of $D$-dimensional loop integrals that are needed to derive observables in classical general relativity from scattering amplitudes. Our approach simplifies the soft-region method of integration by judiciously combining terms before the final integrations. We demonstrate the method by computing the required integrals for black-hole scattering to the second Post-Minkowskian order in Einstein gravity coupled to scalars. We also confirm recent results at the third Post-Minkowskian order regarding universality and high-energy behavior of gravitational interactions in maximal supergravity.

arXiv comment42 pages. v3: version to appear in PRD

References in corpus (33)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• 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
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Lectures on differential equations for Feynman integrals
• High-energy gravitational scattering and the general relativistic two-body problem
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• General Relativity from Scattering Amplitudes
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Eikonal Quantum Gravity and Planckian Scattering
• On-shell Techniques and Universal Results in Quantum Gravity
• Radiative contribution to classical gravitational scattering at the third order in $G$
• All-Order Collinear Behavior in Gauge Theories
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Universality of ultra-relativistic gravitational scattering
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• Radiation Reaction from Soft Theorems
• Bending of Light in Quantum Gravity
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Universality in the classical limit of massless gravitational scattering
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• Second-order Post-Minkowskian scattering in arbitrary dimensions
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level
• Absence of Triangles in Maximal Supergravity Amplitudes
• Integrability of Black Hole Orbits in Maximal Supergravity
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes

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• Dynamical features and shadows of quantum Schwarzschild black hole in effective field theories of gravity
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• The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order
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• Conservative Scattering of Reissner-Nordström Black Holes at Third Post-Minkowskian Order
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• Waveforms from Amplitudes
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• Reduction of Order and Transseries Structure of Radiation Reaction
• $S$-matrix approach to general gravity and beyond
• Classical gravitational scattering from a gauge-invariant double copy
• On two body gravitational scattering within perturbative gravit
• Black Holes in Einstein-scalar-Gauss-Bonnet model probed with scattering amplitudes
• Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
• Quantum gravity phenomenology from the perspective of quantum general relativity and quadratic gravity
• Analytic structure of the high-energy gravitational amplitude: multi-H diagrams and classical 5PM logarithms
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• Effective-one-body formalism for leading-order radiative effects in the post-linear framework