The Effective Field Theorist's Approach to Gravitational Dynamics

TL;DR

This paper presents a comprehensive EFT framework for gravitational dynamics, detailing how long-wavelength gravitational interactions of extended bodies—such as binaries—can be described by a tower of effective theories. By separating scales into potential (binding) and radiation zones and employing the method of regions, multipole expansions, and renormalization group techniques, it derives conservative dynamics, radiation, tail effects, and radiation-reaction effects for both non-spinning and spinning compact objects. Finite-size and tidal effects are encoded via Wilson coefficients, with black holes exhibiting vanishing Love numbers in d=4 while neutron stars retain nonzero tidal responses; spinning bodies introduce additional spin-dependent potentials and waveform corrections. The framework naturally connects to cosmology through a closing section on large-scale structure EFTs, and it provides a versatile toolkit for precision gravitational-wave phenomenology, including higher-PN corrections, tails, and absorption phenomena. Overall, the EFT approach unifies analytical control, systematic power counting, and cross-checks with numerical relativity to improve gravitational-wave templates and tests of gravity in the strong-field regime.

Abstract

We review the effective field theory (EFT) approach to gravitational dynamics. We focus on extended objects in long-wavelength backgrounds and gravitational wave emission from spinning binary systems. We conclude with an introduction to EFT methods for the study of cosmological large scale structures.

Figures (26)

• Figure 1: The dashed line represents the static propagator, with $p_0=0$. In the subsequent diagrams each cross represents an insertion of a factor of $p_0^2/{\boldsymbol{p}}^2$, see \ref{['expP']}.
• Figure 2: Feynman rules. The solid line represents point-like external sources which do not propagate. It is depicted in this fashion for historical reasons, e.g. nrgr.
• Figure 3: Feynman diagrams representing the contributions in \ref{['ja2']} (left) and \ref{['ja12']} (right). The wavy line is the radiation field.
• Figure 4: Feynman diagrams which contribute to the one-point function to ${\cal O}(G_N^3)$nrgr.
• Figure 5: The first diagram accounts for an insertion of $p_0^2$ in \ref{['prpH']}. The subsequent diagrams include velocity corrections from the point-particle action in \ref{['tpphmn']}.