Effective field theory of gravity for extended objects

By Walter D. Goldberger, I. Rothstein. 2004

658 citations recorded by the source corpus.

Using effective field theory (EFT) methods we present a Lagrangian formalism which describes the dynamics of nonrelativistic extended objects coupled to gravity. The formalism is relevant to understanding the gravitational radiation power spectra emitted by binary star systems, an important class of candidate signals for gravitational wave observatories such as LIGO or VIRGO. The EFT allows for a clean separation of the three relevant scales: ${r}_{s}$, the size of the compact objects, $r$, the orbital radius, and $r/v$, the wavelength of the physical radiation (where the velocity $v$ is the expansion parameter). In the EFT, radiation is systematically included in the $v$ expansion without the need to separate integrals into near zones and radiation zones. Using the EFT, we show that the renormalization of ultraviolet divergences which arise at ${v}^{6}$ in post-Newtonian (PN) calculations requires the presence of two nonminimal worldline gravitational couplings linear in the Ricci curvature. However, these operators can be removed by a redefinition of the metric tensor, so that the divergences arising at ${v}^{6}$ have no physically observable effect. Because in the EFT finite size features are encoded in the coefficients of nonminimal couplings, this implies a simple proof of the decoupling of internal structure for spinless objects to at least order ${v}^{6}$. Neglecting absorptive effects, we find that the power counting rules of the EFT indicate that the next set of short distance operators, which are quadratic in the curvature and are associated with tidal deformations, does not play a role until order ${v}^{10}$. These operators, which encapsulate finite size properties of the sources, have coefficients that can be fixed by a matching calculation. By including the most general set of such operators, the EFT allows one to work within a point-particle theory to arbitrary orders in $v$.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d092e3335cbaf78b848df82780374f598d381865

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

Citations in the corpus

On-shell heavy particle effective theories (2020, background): “However, the left hand sides of these equations contradict the latter interpretation; the spinor brackets 〈12〉 and [12] themselves contain spin effects.”
Spinning gravitating objects in the effective field theory in the post-Newtonian scheme (2015, methodology): “We begin by recalling the general setup of an EFT for the binary inspiral problem in terms of a tower of EFTs, building on [12, 13].”
Cosmological non-linearities as an effective fluid (2010, background): “29 This means that one can match our effective theory to the effective theory of black holes by Goldberger and Rothstein [8].”