Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-08T08:53:45.952Z Has data issue: false hasContentIssue false
  • English
  • Français

Geodesies of an affine connection and electromagnetism with radiation reaction

Published online by Cambridge University Press:  17 April 2009

R.R. Burman
R.R. Burman
Affiliation:
University of Western Australia, Nedlands, Western Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper deals with the motion of a point test charge in an external electromagnetic field with the effect of electromagnetic radiation reaction included. The equation of motion applicable in a general Riemannian space-time is written as the geodesic equation of an affine connection. The connection is the sum of the Christoffel connection and a tensor which depends on, among other things, the external electromagnetic field, the charge and mass of the particle and the Ricci tensor. The affinity is not unique; a choice is made so that the covariant derivative of the metric tensor with respect to the connection vanishes. The special cases of conformally flat spaces and the space of general relativity are discussed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 2 , April 1971 , pp. 225 - 240
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Barut, A.O., Electrodynamics and classical theory of fields and particles (The MacMillan Company, New York; Collier-MacMillan, London; 1961).Google Scholar
[2]Burman, R., “Particle paths of general relativity as geodesies of an affine connection”, Bull. Austral. Math. Soc. 3 (1970), 325–335Google Scholar
[3]Burman, R.R., “Paths of charges in general relativity as geodesies of Einstein's non-Riemannian geometry”, Bull. Austral. Math. Soc. 4 (1971), 69–84.CrossRefGoogle Scholar
[4]DeWitt, Bryce S. and Brehme, Robert W., “Radiation damping in a gravitational field”, Ann. Physics 9 (1960), 220–259.Google Scholar
[5]DeWitt, Cécile Morette and DeWitt, Bryce S., “Falling charges”, Physics 1 (1964), 3–20.Google Scholar
[6]Dirac, P.A.M., “Classical theory of radiating electrons”, Proc. Roy. Soc. London Ser. A 167 (1938), 148–169.Google Scholar
[7]Droz-Vincent, P., “Electromagnetism and geodesies”, Nuovo Cimento B 51 (1967), 555–556.Google Scholar
[8]Eddington, A.S., The mathematical theory of relativity, 2nd ed. (Cambridge University Press, Cambridge, 1924).Google Scholar
[9]Einstein, Albert, The meaning of relativity, 6th ed. (Methuen, London, 1956).Google Scholar
[10]Václav Hlavatý, Geometry of Einstein's unified field theory (Noordhoff, Groningen, H.D. [1957]).Google Scholar
[11]Hobbs, J.M., “A vierbein formalism of radiation damping”, Ann. Physics 47 (1968), 141–165.Google Scholar
[12]Hobbs, J.M., “Radiation damping in conformally flat universes”, Ann. Physics 47 (1968), 166–172.Google Scholar
[13]Rohrlich, F., “Solution of the classical electromagnetic self-energy problem”, Phys. Rev. Letters 12 (1964), 375–377.Google Scholar
[14]Rohrlich, F., Classical charged particles. Foundations of their theory (Addison-Wesley, Reading, Massachusetts, 1965).Google Scholar
[15]Rohrlich, F. and Winicour, J., “The equations of motion of a system of charged particles in a gravitational field”, Perspectives in geometry and relativity (Essays in honor of Václav Hlavatý, edited by Banesh Hoffmann), 318–324. (Indiana University Press, Bloomington, London, 1966).Google Scholar
[16]Schrödinger, Erwin, Space-time structure (Cambridge University Press, Cambridge, 1950).Google Scholar
[17]Sen, D.K., “A simple derivation of the geodesic equations of motion from the matter tensor in general relativity using the d-function”, Nuovo Cimento 21 (1961), 184–185.Google Scholar
[18]Sen, D.K., Fields and/or particles (The Ryerson Press, Toronto; Academic Press, London, New York, 1968).Google Scholar
[19]Synge, J.L., Relativity: The general theory (North-Holland, Amsterdam; Interscience, New York; 1960).Google Scholar