Effective field theory of gravity for extended objects
Abstract
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: rs, 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 v6 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 v6 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 v6. 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 v10. 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.
- Publication:
-
Physical Review D
- Pub Date:
- May 2006
- DOI:
- 10.1103/PhysRevD.73.104029
- arXiv:
- arXiv:hep-th/0409156
- Bibcode:
- 2006PhRvD..73j4029G
- Keywords:
-
- 04.25.Nx;
- 04.30.Db;
- 11.10.Gh;
- 11.27.+d;
- Post-Newtonian approximation;
- perturbation theory;
- related approximations;
- Wave generation and sources;
- Renormalization;
- Extended classical solutions;
- cosmic strings domain walls texture;
- High Energy Physics - Theory;
- Astrophysics;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Phenomenology
- E-Print:
- LaTeX 24 pages, 11 figures. Added discussion of field redefinitions. New appendix with Feynman rules