Stephen J Crothers has published 17 articles in
Progress of Physics. One of those papers was co-authored by Jeremy Dunning-Davies, who edited an issue of
The Open Astronomy Journal that's being discussed in the thread that asks "
How did crackpot Electric Universe papers get published in a peer-reviewed journal?" Crothers was sole author of the other 16 papers.
Today I'm going to discuss the very first of those papers:
That paper contains four technical sections, plus a dedication to Leonard S Abrams and an epilogue that explains how Crothers became interested in general relativity through
the Adams paper I discussed previously. The first two technical sections basically repeat what Adams wrote, adding only some snark and a sloppy reformulation (that I believe to be incorrect) of one relatively unimportant formula.
In section 3, Crothers strikes out on his own. Here's what remains of the first half of section 3 after snark, redundancy, and irrelevancy have been excised:
----------->
See the LaTeX enable equations: Here
Several things:
According to (23), at r=r
0, g
00 = 0. Equation (23) says nothing about Φ.
If g00 = 0, then equation (21) says Φ = 1, not ½.
I think Crothers got Φ = ½ by using his "weak far field" approximation under the assumption that C(r
0)=(2m)
2, but that weak field approximation is obviously the wrong formula to use for calculations in the strong field at r=r
0. (Crothers takes that value of the radial coordinate r to be the location of the point mass, when it's actually the event horizon, but that doesn't matter here: it's a strong field either way).
The correct calculation of Φ = 1 appears to refute the main point Crothers is trying to make here. (I'm not entirely sure what point Crothers is trying to make here. Perhaps a physicist could explain it to me. Crothers couldn't.)
Finally, g
00 is coordinate-dependent. (That's an observation, not a criticism, because the gravitational potential has to be coordinate-dependent.) Crothers thinks he's stuffed all of that coordinate-dependence into C(r), but that's true only for coordinate systems that satisfy a number of assumptions. Crothers made some of those assumptions explicit, but quite a few others are implicit. One of those assumptions is that the coordinates take advantage of spherical symmetry so he can ignore all but the time and radial coordinates; that's fine. Another assumption is that the metric is static. That rules out all coordinate systems that cover the event horizon and its spatial interior.
So I don't even believe equation (21) can be true in general.
