Effective Field Theories of Post-Newtonian Gravity: A comprehensive review (1807.01699v3)

Abstract: [Abridged] This review article presents the progress made over the last decade, since the introduction of effective field theories (EFTs) into post-Newtonian (PN) gravity. These have been put forward in the context of gravitational waves (GWs) from the compact binary inspiral. The mature development of this interdisciplinary field has resulted in significant advances of wide interest to physics at several levels serving various purposes. The field has firmly demonstrated, that seemingly disparate physical domains, such as quantum field theory and classical gravity, are related, and that the EFT framework is a universal one, where it has been proven to supply a robust methodology to boost progress in the development of PN theory. The review is aimed at a broad audience, from general readers new to the field, to specialists and experts in related subjects. The review begins with an overview of the introduction of EFTs into classical gravity and their development. Then, the basic ideas, which form the conceptual foundation of EFTs, are provided, and the strategy of a multi-stage EFT framework, which is utilized for the PN binary inspiral problem, is outlined. The main body of the review is then dedicated to presenting in detail the study of each of the effective theories at each of the intermediate scales in the problem, up to the actual GW observables. The review is concluded with the multiple prospects of building on the progress in the field, and using further modern field theory insights and tools, to specifically address the study of GWs, as well as to broadly expand our fundamental understanding of gauge and gravity theories across the classical and quantum regimes.

• The paper introduces a multi-stage effective field theory framework that enhances the precision modeling of binary inspirals in gravitational wave astronomy.
• It details methodological advances including worldline techniques, gauge fixing, and the derivation of high-order post-Newtonian corrections with spin-dependent effects.
• The review highlights practical implications for gravitational wave detection and outlines future research directions linking classical gravity with quantum field methods.

Effective Field Theories of Post-Newtonian Gravity: A Comprehensive Review

The application of effective field theories (EFTs) in the paper of post-Newtonian (PN) gravity has introduced significant methodological advancements in the field, particularly pertinent to the paper of gravitational waves (GWs) from compact binary systems. This review encapsulates the developments in applying EFTs to PN gravity, emphasizing the interdisciplinary convergence of quantum field theory and classical gravity within a unified effective framework.

The integration of EFTs into the domain of PN gravity is not merely academic but supports practical efforts in gravitational wave astronomy. The EFT approach optimizes the theoretical modeling of binary inspirals, crucial for interpreting data from GW detections.

Structure and Achievements of the Review

1. Introduction of EFTs to PN Gravity: The review initiates with historical developments that led to the incorporation of EFTs in PN gravity. It underscores the significance of EFTs for enhancing the PN approximation used in modeling the inspiral phase of compact binaries, where objects exhibit non-relativistic relative speeds.
2. Conceptual Foundations and Multi-Stage Framework: Central to the discussion is the multi-stage EFT framework. The theory progressively integrates physical scales, beginning from the internal scale of a single compact object, advancing to the binary's orbital scale, and culminating with the scale of emitted gravitational radiation. The EFT hierarchy elegantly separates these scales, advocating a systematic perturbative expansion in terms of the small parameter—essentially the orbital velocity divided by the speed of light.
3. Detailed Methodological Advances: The review explores the technical construction of the EFT framework. It discusses worldline approaches, gauge fixing, and Feynman diagrams in detail. Key results include the derivation of high-order PN corrections and spin-dependent effects pivotal for modeling spinning compact objects like black holes and neutron stars. The review elucidates EFTs' role in automating such complex derivations, mentioning the ‘EFTofPNG’ code, which collates computational techniques for deriving PN dynamics inclusively.
4. Radiative Sector and Implications: Significant contributions to understanding radiation reaction and hereditary effects like tail and memory effects are presented. The classical renormalization group flow emerges from these considerations, drawing parallels between classical gravitational systems and quantum field renormalization concepts.
5. Future Prospects: Looking forward, the review contemplates expanding EFT applications in PN gravity, particularly addressing gaps in non-conservative sectors and the inclusion of higher-order spinning interactions. It anticipates employing more recent field-theoretic methodologies, such as scattering amplitude techniques, to bridge PN theory with quantum gravity prospects.

Implications and Future Developments

By linking QFT methods with classical gravity problems, EFTs have broadened the toolbox for theoretical physicists tackling the complex and computationally intensive problem of GW emission from binary systems. The review positions EFTs as not only a method for high-precision calculations but a conduit for theoretical exploration within and beyond general relativity.

Further research suggested in the review indicates potential for investigating extensions to general relativity, considering massive gravitons, scalar fields, or higher dimensions. The insights gleaned from applying EFTs could help resolve longstanding questions about the fundamental nature of gravity, perhaps providing clues relevant to quantum gravity or dark matter.

In conclusion, the review articulates a compelling narrative of the symbiotic relationship between classical gravity, quantum field theories, and gravitational wave physics. The systematic and methodical treatment of multi-scale problems through EFT is shown to significantly advance our understanding and capability in precision gravitational wave astronomy, with perspectives that could extend into addressing broader concepts in physics.