2008/01/31 by Chad R. Galley, B. L. Hu · 1 citation
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Classical mechanics #Curvature #Geometry #Gravitation #Gravitational wave #Graviton #Mathematical physics #Minkowski space #Physics #Point particle #Propagator #Pulsars and Gravitational Waves Research #Quantum mechanics #Regularization (linguistics) #Spacetime #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.79.064002
published as Phys.Rev.D79:064002,2009 · 22 pages, 5 figures; references added, revised Appendices B & C, corrected typos, revisions throughout for clarification particularly in Section IV.B; submitted to PRD
arxiv created 2008/06/05 · openalex publication_date 2009/03/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this series we construct an effective field theory (EFT) in curved spacetime to study gravitational radiation and backreaction effects. We begin in this paper with a derivation of 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, which in this problem are the size of the compact object rm and the radius of curvature of the background spacetime R such that \ensuremathε\ensuremath≡rm/R\ensuremath≪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 partie finie to isolate the nonlocal finite part from the quasilocal 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 a first 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(\ensuremathε4), in the form of an effacement principle. The relatively large radius-to-mass ratio of a white dwarf star allows for these effects to be enhanced until the white dwarf becomes tidally disrupted, a potentially O(\ensuremathε2) process, or plunges into the supermassive black hole. This work provides a new foundation for further exploration of higher order self-force corrections, gravitational radiation, and spinning compact objects.