Gravitational radiative corrections from effective field theory

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.

Tail effect in gravitational radiation reaction: Time nonlocality and renormalization group evolution

“…The spin-spin gravitational potentials to 3PN were obtained within the EFT approach in [11][12][13][14]18], and in [25][26][27][28] and [29], using the ArnowittDeser-Misner (ADM) and harmonic gauge formalisms, respectively. The radiative multipole moments quadratic in the spin needed for the radiated power to 3PN, computed in [16] using the framework of [8,10,14,30], were also obtained in [29], although the comparison is pending. The required multipoles for the gravitational wave amplitude to 2.5PN order were computed in [17]; see also [31].…”

“…The IR singularities (which are also present in the leading tail contribution) exponentiate into an overall phase in the amplitude [8], which drops out of the total radiated power or can be removed from the gravitational waveform via a time redefinition [17]. On the other hand, the UV divergences thus far have been properly renormalized through counterterms in the radiation theory, which led to renormalization group (RG) trajectories for the binding mass and multipole moments, described in [8,56]. As we discuss here, similar behavior unfolds through the study of radiation-reaction effects, albeit involving a subtle interplay between the theory of potential modes (near zone) and the radiation sector (far zone).…”

“…The radiation-reaction force corrects the dynamics of the constituents of the binary system at the orbit scale, r. However, we compute it by integrating out the radiation field,h μν , with a long-distance effective action [8,30] S rad eff ½x a ;…”

“…[4][5][6] (see [7] for a complete list of references.) On the other hand, in the radiative sector, the 1PN [8] and 2PN [9] radiative multipoles were computed within NRGR, which is however still below the state-of-the-art for nonspinning binary systems at 3PN order, e.g. [7].…”

Experimental mathematics meets gravitational self-force

“…Additionally, note that Nickel [40] makes similar predictions of leading logarithmic-type terms to arbitrarily high orders for the ground state energy of H + 2 , and is able to derive some of them. Finally, these sorts of predictions of leading logarithms to arbitrarily high orders are likely related to the multipole moment beta functions discussed by Goldberger et al [66,67], where they predict the coefficient of the first occurrence of a given power of a logarithm in both the energy flux and the binding energy using the beta function for the dominant (2, 2) mode.…”