Hostname: page-component-cb9f654ff-kl2l2 Total loading time: 0 Render date: 2025-08-20T06:18:45.381Z Has data issue: false hasContentIssue false
  • English
  • Français

Paths of charges in general relativity as geodesics of Einstein's non-Riemannian geometry

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.

The equation of motion of charged incoherent matter, and hence of a test charge, in general relativity can be written as the geodesic equation of an affine connection. Here, the connection is chosen to satisfy a condition which has the form of one of the basic geometrical principles of Einstein's unified field theory. The symmetric part of the fundamental tensor of the geometry is chosen to be the metric tensor of general relativity; equations to be satisfied by the skew part, involving the electromagnetic field, are obtained. An alternative condition on the affinity is also considered.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 1 , February 1971 , pp. 69 - 84
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Bondi, H., “Relativity”, Rep. Progr. Phys. 22 (1959), 97–120.CrossRefGoogle Scholar
[2]Bose, S.N., “The affine connection in Einstein's new unitary field theory”, Ann. of Math. (2) 59 (1954), 171–176.CrossRefGoogle Scholar
[3]Burman, R., “Particle paths of general relativity as geodesics of an affine connection”, Bull. Austral. Math. Soc. 3 (1970), 325–335.CrossRefGoogle Scholar
[4]Droz-Vincent, P., “Electromagnetism and geodesics”, Nuovo Cimento B 51 (1967), 555–556.CrossRefGoogle Scholar
[5]Einstein, Albert, The meaning of relativity, 6th ed. (Methuen, London, 1956).Google Scholar
[6]Einstein, A. and Kaufman, B., “Algebraic properties of the field in the relativistic theory of the asymmetric field”, Ann. of Math. (2) 59 (1954), 230–244.CrossRefGoogle Scholar
[7]Einstein, A. and Kaufman, B., “A new form of the general relativistic field equations”, Ann. of Math. (2) 62 (1955), 128–138.CrossRefGoogle Scholar
[8]Hlavatý, Václav, “The elementary basic principles of the unified theory of relativity. B”, J. Rational Mech. Anal. 2 (1953), 1–52.Google Scholar
[9]Hlavatý, Václav, “The elementary basic principles of the unified theory of relativity. B 2”, J. Rational Mech. Anal. 4 (1955), 247–277.Google Scholar
[10]Hlavatý, Václav, “The elementary basic principles of the unified theory of relativity. B 3”, J. Rational Mech. Anal. 4 (1955), 653–679.Google Scholar
[11]Hlavatý, Václav, Geometry of Einstein's unified field theory (Noordhoff, Groningen, 1957).Google Scholar
[12]Hlavatý, V. and Sáenz, A.W., “Uniqueness theorems in the unified theory of relativity”, J. Rational Mech. Anal. 2 (1953), 523–536.Google Scholar
[13]Kaufman, B., “Mathematical structure of the non-symmetric field theory”, Jubilee of relativity theory: Proceedings of a Conference held in Berne, July, 1955. Helv. Phys. Acta. Suppl. IV, 227–238. (Birkhäuser Verlag, Basel, 1956.)Google Scholar
[14]Schrödinger, Erwin, Space-time structure (Cambridge University Press, Cambridge, 1950).Google Scholar
[15]Sen, D.K., “A simple derivation of the geodesic equations of motion from the matter tensor in general relativity using the δ-function”, Nuovo Cimento 21 (1961), 184–185.CrossRefGoogle Scholar
[16]Sen, D.K., Fields and/or particles (The Byerston Press, Toronto; Academic Press, London, New York, 1968).Google Scholar
[17]Tonnelat, Marie-Antoinette, La théorie du champ unifié d'Einstein et quelques-uns de ses développements (Gauthier-Villars, Paris, 1955).Google Scholar
[18]Tonnelat, Marie-Antoinette, “Les espoirs et les difficultés de la théorie du champ unifié d'Einstein”, Recent developments in general relativity, 107–118. (Pergamon, Oxford; PWN-Polish Scientific Publishers, Warszawa, 1962).Google Scholar