# Reissner-Nordström repulsion

by bcrowell
Tags: reissnernordström, repulsion
 P: 202 Not really answering your question directly, but a related discussion which may be useful - namely the apparently repulsive field of a charged mass point is discussed by Pekeris: http://www.pnas.org/content/79/20/6404.full.pdf
PF Patron
Emeritus
P: 5,322
 Quote by sheaf Not really answering your question directly, but a related discussion which may be useful - namely the apparently repulsive field of a charged mass point is discussed by Pekeris: http://www.pnas.org/content/79/20/6404.full.pdf
Thanks, for the reply, Sheaf. However, when I click on the link I get an error. Do you have a reference so that maybe I could find an abstract by googling?

-Ben

P: 202

## Reissner-Nordström repulsion

 Quote by bcrowell Thanks, for the reply, Sheaf. However, when I click on the link I get an error. Do you have a reference so that maybe I could find an abstract by googling? -Ben
Bizarre, I can't get to it now either, but I could this morning. Sorry about that. Maybe there's a server problem. A google search which will bring up that link is "gravitational field point charge pekeris". If you don't have any luck and can't get to it, PM me and I can mail a copy.

Basically he discusses the surprising repulsive force that you get when M=0 in Reissner Nordstrom, then argues that this is unrealistic because with the charge present, there will be always an equivalent electromagnetic mass, consequently the field ends up being attractive !
 PF Patron Sci Advisor Emeritus P: 5,322 I see, thanks! But I guess this doesn't say anything about the nonzero mass case.
P: 202
 Quote by bcrowell I see, thanks! But I guess this doesn't say anything about the nonzero mass case.

No, I guess it doesn't. It seems to be a restatement of your abstract number 1 above. His abstract states (sorry, the copy from the pdf screws up the mathematical notation, and I'm too lazy to Latex it !)

 Adopting, with Schwarzschild, the Einstein gauge (lg_mu_nul = -1), a solution of Einstein's field equations for a charged mass point of mass M and charge Q is derived, which differs from the Reissner-Nordstr0m solution only in that the variable r is replaced by R = (r^3 + a^3)^1/3, where a is a constant. The Newtonian gravitational potential psi = (2/c^2)(l - goo) obeys exactly the Poisson equation (in the R variable), with the mass density equal to (E^2/4mc^2), E denoting the electric field. Psi also obeys a second linear equation in which the operator on psi, is the square root of the Laplacian operator. The electrostatic potential phi (= Q/R), A, and all the components of the curvature tensor remain finite at the origin of coordinates. The electromagnetic energy of the point charge is finite and equal to (Q2/a). The charge Q defines a pivotal mass M* = (Q/G^1/2). IfM < M*, then the whole mass is electromagnetic. If M > M*, the electromagnetic part of the mass M_em equals [M - (M^2 - M*^2)^1/2], whereas the material part of the mass M_em equals (M^2 - M*^2)^1/2. When M > M*, the constant a is determined following Schwarzschild, by shrinking the "Schwarzschild radius" to zero. When M < M*, a is determined so as to make the gravitational acceleration vanish at the origin.
Good point you make about defining repulsion in a covariant manner.

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