Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-07-29
Phys.Rev.D81:024023,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
44 pages, 4 figures
Scientific paper
10.1103/PhysRevD.81.024023
I review the problem of motion for small bodies in General Relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed; I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body's past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long timescales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.
No associations
LandOfFree
The self-consistent gravitational self-force does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The self-consistent gravitational self-force, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The self-consistent gravitational self-force will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-522226