Black hole binary dynamics from the double copy and effective theory

Zvi Bern,Mao Zeng,Chia-Hsien Shen,Clifford Cheung,Mikhail P Solon,Radu Roiban

doi:10.1007/jhep10(2019)206

Abstract

We describe a systematic framework for computing the conservative potential of a compact binary system using modern tools from scattering amplitudes and effective field theory. Our approach combines methods for integration and matching adapted from effective field theory, generalized unitarity, and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. With these methods we derive the third post-Minkowskian correction to the conservative two-body Hamiltonian for spinless black holes. We describe in some detail various checks of our integration methods and the resulting Hamiltonian.

Highlights

The extraordinary detection of gravitational waves by the LIGO and Virgo collaborations [1, 2] has opened a new window into the cosmos
The LIGO and Virgo detectors boast an exquisite precision which will grow in future upgrades, demanding commensurately accurate theoretical predictions encoded in waveform templates utilized for detection and extraction of source parameters
These waveforms are constructed from an array of complementary approaches, including the effective one-body (EOB) formalism [3, 4], numerical relativity [5,6,7], the self-force formalism [8, 9], and a number of perturbative methods for the inspiral phase, including the post-Newtonian (PN) [10, 11] and post-Minkowskian (PM) [12,13,14,15,16,17,18,19,20,21,22] approximations, as well as the nonrelativistic general relativity (NRGR) formalism [23] based on effective field theory (EFT)

Summary

Introduction

The extraordinary detection of gravitational waves by the LIGO and Virgo collaborations [1, 2] has opened a new window into the cosmos. The LIGO and Virgo detectors boast an exquisite precision which will grow in future upgrades, demanding commensurately accurate theoretical predictions encoded in waveform templates utilized for detection and extraction of source parameters These waveforms are constructed from an array of complementary approaches, including the effective one-body (EOB) formalism [3, 4], numerical relativity [5,6,7], the self-force formalism [8, 9], and a number of perturbative methods for the inspiral phase, including the post-Newtonian (PN) [10, 11] and post-Minkowskian (PM) [12,13,14,15,16,17,18,19,20,21,22] approximations, as well as the nonrelativistic general relativity (NRGR) formalism [23] based on effective field theory (EFT). Further improvements in high-precision theoretical predictions from general relativity will be essential given expected improvements in detector sensitivity

Objectives

Methods

Discussion

Conclusion