General Relativity from Intersection Theory

Abstract

This paper combines the post-Minkowskian expansion of general relativity with the language of intersection theory. Because of the nature of the soft limit inherent to the post-Minkowskian expansion, the intersection-based approach is of enhanced utility in that theory compared to a generic quantum field theory. In the language of intersection theory, Feynman integrals are rephrased in terms of twisted cocycles. The intersection number is a pairing between two such cocycles and its existence allows for the direct projection onto a basis of master integrals. In this paper we use this approach to compute the second post-Minkowskian contribution to the scattering of two compact astronomical objects, getting results in agreement with previous findings.

Ten pages, two figures

References in corpus (8)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Duals of Feynman Integrals, 2: Generalized Unitarity
• Cosmology meets cohomology
• Calabi-Yau meets Gravity: A Calabi-Yau three-fold at fifth post-Minkowskian order
• Correlation functions on the lattice and twisted cocycles

Cited by in corpus (4)

• Classifying post-Minkowskian geometries for gravitational waves via loop-by-loop Baikov
• Intersection Numbers from Companion Tensor Algebra
• Classification of Feynman integral geometries for black-hole scattering at 5PM order
• Differential equations for tree--level cosmological correlators with massive states