dorsal/arxiv
View SchemaAsymptotic conditions of motion for radiating charged particles
| Authors | James L. Anderson |
|---|---|
| Categories | |
| ArXiv ID | physics/9709031 |
| URL | https://arxiv.org/abs/physics/9709031 |
| DOI | 10.1103/PhysRevD.56.4675 |
Abstract
Approximate asymptotic conditions on the motion of compact, electrically charged particles are derived within the framework of general relativity using the Einstein- Infeld-Hoffmann (EIH) surface integral method. While superficially similar to the Abraham-Lorentz and Lorentz-Dirac (ALD) equations of motion, these conditions differ from them in several fundamental ways. They are not equations of motion in the usual sense but rather a set of conditions which these motions must obey in the asymptotic future of an initial value surface. In addition to being asymptotic, these conditions of motion are approximate and apply, as do the original EIH equations, only to slowly moving systems. Also, they do not admit the run- away solutions of these other equations. As in the original EIH work, they are integrability conditions gotten from integrating the empty-space (i.e., source free) Einstein-Maxwell equations of general relativity over closed two-surfaces surrounding the sources of the fields governed by these equations. No additional ad hoc assumptions, such as the form of a force law or the introduction of inertial reaction terms, needed to derive the ALD equations are required for this purpose. Nor is there a need for any of the infinite mass renormalizations that are required in deriving these other equations.
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"abstract": "Approximate asymptotic conditions on the motion of compact, electrically\ncharged particles are derived within the framework of general relativity using\nthe Einstein- Infeld-Hoffmann (EIH) surface integral method. While\nsuperficially similar to the Abraham-Lorentz and Lorentz-Dirac (ALD) equations\nof motion, these conditions differ from them in several fundamental ways. They\nare not equations of motion in the usual sense but rather a set of conditions\nwhich these motions must obey in the asymptotic future of an initial value\nsurface. In addition to being asymptotic, these conditions of motion are\napproximate and apply, as do the original EIH equations, only to slowly moving\nsystems. Also, they do not admit the run- away solutions of these other\nequations. As in the original EIH work, they are integrability conditions\ngotten from integrating the empty-space (i.e., source free) Einstein-Maxwell\nequations of general relativity over closed two-surfaces surrounding the\nsources of the fields governed by these equations. No additional ad hoc\nassumptions, such as the form of a force law or the introduction of inertial\nreaction terms, needed to derive the ALD equations are required for this\npurpose. Nor is there a need for any of the infinite mass renormalizations that\nare required in deriving these other equations.",
"arxiv_id": "physics/9709031",
"authors": [
"James L. Anderson"
],
"categories": [
"physics.class-ph"
],
"doi": "10.1103/PhysRevD.56.4675",
"title": "Asymptotic conditions of motion for radiating charged particles",
"url": "https://arxiv.org/abs/physics/9709031"
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