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.
Similar content being viewed by others
References
Reissner, H.: Über die Eigengravitation des elektrischen Feldes nach der Einstein’schen Theorie. Ann. Phys. 50, 106–120 (1916)
Nordström, G.: On the energy of the gravitational field in Einstein’s theory. Verh. K. Ned. Akad. Wet. Afd. Natuurkd. 26, 1201–1208 (1918)
Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973), pp. 156–161
Henry, R.C.: Kretschmann scalar for a Kerr-Neuman black hole. Astrophys. J. 535, 350–353 (2000)
de la Cruz, V., Israel, W.: Gravitational bounce. Nuovo Cimento 51, 744 (1967)
Cohen, J.M., Gautreau, D.G.: Naked singularities, event horizon, and charged particles. Phys. Rev. D 19, 2273–2279 (1979)
Hiscock, W.A.: On the topology of charged spherical collapse. J. Math. Phys. 22, 215 (1981)
de Felice, F., Clarke, C.J.S.: Relativity on Curved Manifolds. Cambridge University Press, Cambridge (1992), pp. 369–372
Synge, J.L.: Relativity: The General Theory. North-Holland, Amsterdam (1966), Chap. VII, §5 and Chap. X, §4
Gautreau, R., Hoffman, R.B.: The structure of the sources of Weyl-type electrovac fields in general relativity. Nuovo Cimento 16, 162–171 (1973)
Whittaker, E.T.: On Gauss theorem and the concept of mass in general relativity. Proc. R. Soc. Lond. A 149, 384 (1935)
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)
Eisenhart, L.P.: Riemannian Geometry. Princeton University Press, Princeton (1997), p. 41
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Marsh, G.E. Charge, Geometry, and Effective Mass. Found Phys 38, 293–300 (2008). https://doi.org/10.1007/s10701-008-9209-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-008-9209-1