Self-consistent gravitational self-force
- Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1 (Canada)
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 time scales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.
- OSTI ID:
- 21413389
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 81, Issue 2; Other Information: DOI: 10.1103/PhysRevD.81.024023; (c) 2010 The American Physical Society; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
BUFFERS
COMPARATIVE EVALUATIONS
DISTURBANCES
EINSTEIN FIELD EQUATIONS
EQUATIONS OF MOTION
EXPANSION
GENERAL RELATIVITY THEORY
PERTURBATION THEORY
SIMULATION
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
EVALUATION
FIELD EQUATIONS
FIELD THEORIES
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
RELATIVITY THEORY