Effective field theory of gravity for extended objects

Abstract

We present an Effective Field Theory (EFT) formalism which describes the dynamics of non-relativistic extended objects coupled to gravity. The formalism is relevant to understanding the gravitational power spectra emitted by binary star systems, an important class of candidate signals for LIGO and VIRGO. The EFT allows for a clean separation of the long wavelength gravitational dynamics from the details of the internal structure that resolves the delta function singularities associated with the point particle limit. We show that the v^6 ambiguity that plagues the conventional post-Newtonian (PN) calculations (where v is the expansion parameter) can be attributed to the presence of two non-minimal worldline operators linear in the Ricci curvature. 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. 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, do not play a role until order v^10. The coefficients of these point-particle operators exhibit non-trivial classical renormalization group flows whose exact form is encoded in the Schwarzschild solution. Our effective theory generalizes previous approaches to the description of gravity as an EFT by systematically separating classical from quantum effects and thus allowing for arbitrarily large source masses while still retaining manifest power counting at the level of the individual Feynman diagrams.

Keywords

Affiliated Institutions

• Carnegie Mellon University US
• Yale University US

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