Gravitational radiative corrections from effective field theory (0912.4254v3)

Abstract: In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures "post-Minkowskian" corrections to the multipole expansion due to non-linear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from non-relativistic binaries, including long distance effects up to 3PN ($v^6$) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.

Gravitational Radiative Corrections from Effective Field Theory

The paper by Goldberger and Ross offers a comprehensive exploration of gravitational radiative corrections through the lens of Effective Field Theory (EFT). The primary goal is to innovate a theoretical framework capable of elucidating long wavelength gravitational radiation emanating from compact systems. The focus is on the leading order EFT, which adopts the form of a multipole expansion described through a diffeomorphism invariant point particle Lagrangian.

A distinguishing feature of this paper is the incorporation of "post-Minkowskian" corrections, which account for nonlinear general relativity effects that deviate from the standard multipole expansion. The authors particularly address long distance corrections stemming from the interplay between the monopole and quadrupole moments, considering up to two mass insertions. This introduces a practical framework for understanding the corrections in gravitational wave observations from systems such as non-relativistic binaries.

The mathematical rigor underlying this paper is profound. The authors encounter both logarithmic divergences at short distances (UV divergences) and at long wavelengths (IR divergences). They effectively demonstrate that the UV divergences can be absorbed via renormalization of the multipole moments and can be resummed through the renormalization group. This brings to light the theoretical consistency of the renormalization process in gravitational contexts. The IR divergences, however, are shown to effectively cancel out from physically defined observables.

As a testament to the robustness of this formalism, the authors apply the EFT to reproduce several post-Newtonian (PN) corrections to the gravitational wave energy flux, specifically for binaries at rest. Crucially, their results affirm that the scale factorization suggested in prior work by Goldberger and Rothstein stands valid up to the order 3PN (velocity $\sim v^6$).

This paper advances the theoretical understanding of gravitational radiation in several ways:

1. Analytical Techniques: The utilization of EFT to describe gravitational interactions acknowledges the complexity of the two-body problem in general relativity, which is notably nonlinear and often necessitates numerical methods. This work provides analytical solutions in certain regimes, demonstrating a clear hierarchy of scales conducive to perturbative techniques.
2. Renormalization in Gravitation: The treatment of UV divergences applies the renormalization processes familiar in particle physics, showcasing how EFT can be harnessed to address singularities in gravitational calculations. The derivation of consistent RG equations is pivotal for examining scale-independent phenomena in gravitational systems.
3. Post-Minkowskian Corrections: By unifying post-Minkowskian corrections into the model, the paper draws a more precise picture of gravitational radiation influenced by systemic components like mass moments. This enhances predictive capabilities and provides a foundational tool for understanding waveforms in gravitational wave astronomy.

The theoretical implications are profound, offering insights into the examination of complex gravitational systems, particularly with upcoming advancements in gravitational wave detectors such as LIGO and Virgo. Practically, this research paves the way for improved precision in gravitational wave modeling, with potential future applications in isolating effects from specific gravitational interactions and better understanding astrophysical processes.

In conclusion, by merging tools from particle physics with gravitational physics, Goldberger and Ross contribute significantly to theoretical physics, building a robust framework for analyzing gravitational radiation from compact astrophysical systems. Their work sets the stage for further refinement in theoretical gravitational physics, potentially influencing gravitational wave astronomy's future endeavors.