Advertisement

Foundations of Physics

, Volume 38, Issue 3, pp 293–300 | Cite as

Charge, Geometry, and Effective Mass

  • Gerald E. MarshEmail author
Article

Abstract

Charge, like mass in Newtonian mechanics, is an irreducible element of electromagnetic theory that must be introduced ab initio. Its origin is not properly a part of the theory. Fields are then defined in terms of forces on either masses—in the case of Newtonian mechanics, or charges in the case of electromagnetism. General Relativity changed our way of thinking about the gravitational field by replacing the concept of a force field with the curvature of space-time. Mass, however, remained an irreducible element. It is shown here that the Reissner-Nordström solution to the Einstein field equations tells us that charge, like mass, has a unique space-time signature.

Keywords

Reissner-Nordström Charge Curvature 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Reissner, H.: Über die Eigengravitation des elektrischen Feldes nach der Einstein’schen Theorie. Ann. Phys. 50, 106–120 (1916) CrossRefGoogle Scholar
  2. 2.
    Nordström, G.: On the energy of the gravitational field in Einstein’s theory. Verh. K. Ned. Akad. Wet. Afd. Natuurkd. 26, 1201–1208 (1918) Google Scholar
  3. 3.
    Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973), pp. 156–161 zbMATHGoogle Scholar
  4. 4.
    Henry, R.C.: Kretschmann scalar for a Kerr-Neuman black hole. Astrophys. J. 535, 350–353 (2000) CrossRefADSGoogle Scholar
  5. 5.
    de la Cruz, V., Israel, W.: Gravitational bounce. Nuovo Cimento 51, 744 (1967) CrossRefADSGoogle Scholar
  6. 6.
    Cohen, J.M., Gautreau, D.G.: Naked singularities, event horizon, and charged particles. Phys. Rev. D 19, 2273–2279 (1979) CrossRefADSGoogle Scholar
  7. 7.
    Hiscock, W.A.: On the topology of charged spherical collapse. J. Math. Phys. 22, 215 (1981) CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    de Felice, F., Clarke, C.J.S.: Relativity on Curved Manifolds. Cambridge University Press, Cambridge (1992), pp. 369–372 zbMATHGoogle Scholar
  9. 9.
    Synge, J.L.: Relativity: The General Theory. North-Holland, Amsterdam (1966), Chap. VII, §5 and Chap. X, §4 Google Scholar
  10. 10.
    Gautreau, R., Hoffman, R.B.: The structure of the sources of Weyl-type electrovac fields in general relativity. Nuovo Cimento 16, 162–171 (1973) CrossRefGoogle Scholar
  11. 11.
    Whittaker, E.T.: On Gauss theorem and the concept of mass in general relativity. Proc. R. Soc. Lond. A 149, 384 (1935) zbMATHADSCrossRefGoogle Scholar
  12. 12.
    Arnowitt, R., Deser, S., Misner, C.W.: The dynamics of general relativity. In: Witten, L. (ed.) Gravitation: An Introduction to Current Research, pp. 227–265. Wiley, New York (1962) Google Scholar
  13. 13.
    Eisenhart, L.P.: Riemannian Geometry. Princeton University Press, Princeton (1997), p. 41 Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Argonne National Laboratory (Ret)ChicagoUSA

Personalised recommendations