Classical Electron in General Relativity

Phys. Rev. 137, B1385 – Published 8 March 1965
R. Penney


The usual field equations of general relativity are modified to provide for the existence of electrons. The resulting equations, viz., Rμν-14Rgμν=-k(Tμν-14Tgμν), are considered to be microscopically true. The macroscopic averages of the equations are the usual Einstein field equations. On the basis of the field equations, it is shown that an electron may be constructed which is stable and has a momentum and energy which form a four-vector. The electron is held together by the gradient of the Gaussian curvature and is 34 electro magnetic, ¼ gravitational energy. The radiation reaction problem is examined, and it is shown that the Cauchy problem for the field equations is nonregular in the sense that, as with the Lorentz-Dirac equation, one component of the initial acceleration of the electron must be specified. An interesting consequence of the field equations is that a purely electric (static) electron is not a regular solution. The future development of such a particle is not determined. Thus, a spherically symmetric electron must be dynamic in character, i.e., have currents and consequent magnetic moments.


  • Received 10 July 1964
  • Published in the issue dated March 1965

© 1965 The American Physical Society

Authors & Affiliations

R. Penney

  • Scientific Laboratory, Ford Motor Company, Dearborn, Michigan

References (Subscription Required)

Authorization Required


Download & Share

PDF Export Citing Articles (5)



Log In



Article Lookup
Paste a citation or DOI

Enter a citation
  1. Enter a citation to look up or terms to search.

    Ex: "PRL 112 068103", "Phys. Rev. Lett. 112, 068103", "10.1103/PhysRevLett.112.068103"