**Authors**: Chad R. Galley, B. L. Hu

**Date**: 7 Jan 2008

**Abstract**: We construct an effective field theory (EFT) to derive the self-force on a compact object moving in the background spacetime of a supermassive black hole. The EFT approach utilizes the disparity between two length scales, the size of the compact object $r_m$ and the radius of curvature of the background spacetime $\cR$ such that $\mu \equiv r_m / \cR \ll 1$, to treat the orbital dynamics of the compact object, described as an effective point particle, separately from its tidal deformations. The equation of motion of an effective relativistic point particle coupled to the gravitational waves generated by its motion in a curved background spacetime can be derived without making a slow motion or weak field approximation, as was assumed in earlier EFT treatment of post-Newtonian binaries. Ultraviolet divergences are regularized using Hadamard's {\it partie finie} to isolate the non-local finite part from the quasi-local divergent part. The latter is constructed from a momentum space representation for the graviton retarded propagator and is evaluated using dimensional regularization in which only logarithmic divergences are relevant for renormalizing the parameters of the theory. As an important application of this framework we explicitly derive the first order self-force given by Mino, Sasaki, Tanaka, Quinn and Wald. Going beyond the point particle approximation, to account for the finite size of the object, we demonstrate that for extreme mass ratio inspirals the motion of a compact object is affected by tidally induced moments at $O(\muˆ4)$, in the form of an Effacement Principle. This work provides a new foundation for further exploration of higher order self force corrections, gravitational radiation and spinning compact objects.

0801.0900
(/preprints)

2008-01-07, 20:02
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*