## Draft paper deriving a non-empty, stationary, axisymmetric solution solution of Einstein's Equations, based on the Lorentz Force Law

Dear friends at SPR,

I have just posted a DRAFT paper to:

http://home.nycap.rr.com/jry/Papers/...ce%20Paper.pdf

This paper is titled: "Is the Lorentz Force Law Based Upon a Relation
Between rho=mu+p Perfect Fluids and alpha=1 Kerrighan-Type Electromagnetic
Energy Tensors?"

I would appreciate your review and comment on this draft before I consider
next steps.

The abstract is as follows:

It is demonstrated how the Lorentz force law is a direct consequence of
relating a perfect fluid tensor T^uv_Euler for which the rest mass
density rho is related to the energy density me and pressure p according
to rho=mu+p, with an electromagnetic energy tensor T^uv with certain
uniqueness conditions established by Kerrighan in the early-1980s, and
by in turn relating both of these tensors with the Einstein tensor R^uv
- ½ g^uvR. We then use these relationships -- which are effectively the
first integral of the Lorentz force law -- to first establish the metric
tensor g_uv using the known general solution for a non-empty stationary
axisymmetric perfect fluid, and then, to specify the electromagnetic
fields underlying the structure of this perfect fluid for which the
equation of motion is the Lorentz force law. The key advance, is
showing that a solution does exist to the Einstein equations which is
fully compatible with, and indeed is based upon, the Lorentz force law.

I do want to emphasize that this is a work in progress. But, it is now
developed far enough that a posting seeking input is warranted at this time.

Very truly yours,

Jay R. Yablon
_____________________________
Jay R. Yablon
Email: jyablon@nycap.rr.com

 PhysOrg.com physics news on PhysOrg.com >> Promising doped zirconia>> New X-ray method shows how frog embryos could help thwart disease>> Bringing life into focus
 On 2006-04-05, Jay R. Yablon wrote: > I have just posted a DRAFT paper to: > > http://home.nycap.rr.com/jry/Papers/...ce%20Paper.pdf > > This paper is titled: "Is the Lorentz Force Law Based Upon a Relation > Between rho=mu+p Perfect Fluids and alpha=1 Kerrighan-Type Electromagnetic > Energy Tensors?" > > I would appreciate your review and comment on this draft before I consider > next steps. Dear Jay, your paper draft is 30 pages long. Which is too long for me, and I'm sure many other s.p.r patrons, to read in detail. If you really want feed back, you may be interested in the following exercise in efficient communication. Can you summarize the technical (mathematical) content of your work in one paragraph? In advance, I can't necessarily say that this will be possible. But you won't know unless you try. It is also a good test of whether your terminology is standard enough to be recognizable by people familiar with the mathematical background. Perhaps in another paragraph, can you summarize the physical interpretation of your technical results? Usually, this involves relating mathematical objects to things we can measure in the lab. At this stage, you should also consider consistency with known physics and possible measurable predictions. Igor

## Draft paper deriving a non-empty, stationary, axisymmetric solution solution of Einstein's Equations, based on the Lorentz Force Law

Igor Khavkine has offered some sage advice. I would add the following.

Suppose I posted a 30-page paper, obscurely written and packed
with complicated, unmotivated calculations. Suppose the paper ended
with a statement to the effect that I hadn't bothered to think carefully
about its physical implications, but I felt that there might be some.
("The physical viability of these results will need to be considered
over time.") Would Mr. Yablon invest the months which would be required
in working through it? If not, is it realistic to expect anyone to do
so?

Nevertheless, I did take a look at it. I think it is full of
questionable statements, including errors which are both elementary and
serious.

The questionable points are too numerous to catalog here, so I'll
just mention one. Anyone thinking of investing the time to read it
carefully should check this one out first because it is a definite error
at the heart of his argument and easy to check. It occurs on p. 8, just
before equation (5.1).

To explain this error, I quote from another post of his:

> But again, the approach I am taking -- and again, it may take some
> getting used to and I certainly want to make sure it is at most
> unusual but not "illegal" -- is not to add tensor properties, but to
> set one tensor equal to another which thereby constrains each one.
> In fact, I am setting three tensors all to one another: 1) The
> Maxwell tensor with an extra "variable Lambda" term based on
> Kerrighan, 2) the perfect fluid tensor with rho = mu + p (i.e.,
> specific enthalpy = 1), and 3) G^uv. The first derivative of this
> equality is the Lorentz force law; the solution to Einstein's
> equations for this equality yields the spacetime geometry of "a
> perfect fluid which moves according to the Lorentz force law."
> Perhaps when fully developed, we will find that such "a perfect
> fluid which moves according to the Lorentz force law" actually has
> the properties of some real physical entities already known in
> nature.

What he calls the "Maxwell tensor" is the usual energy-momentum
tensor for an electromagnetic field plus a multiple of the identity.

[It probably won't be obvious to many readers that the tensor of
equation (5.1) really is of this form, but if you work it out, you
will see that it is. I happen to be particularly familiar with such
tensors, so I was able to spot this easily. That is the reason for
this post---to save others time by sharing my limited expertise.]

This tensor is a linear transformation which has two distinct
eigenvalues, each with multiplicity 2 (except in the trivial case in
which the tensor vanishes). His "perfect fluid tensor" is diag{mu, p,
p, p}, and so has an eigenvalue p with multiplicity either 3 or 4. Thus
the "Maxwell tensor" cannot equal the "perfect fluid tensor" except in
the trivial case in which both vanish.

Note also that a "perfect fluid tensor" singles out a distinguished
timelike direction, namely the direction of the eigenvector for
eigenvalue mu (except in the degenerate case in which mu = p). So his
analysis contains the hidden assumption that at each point of spacetime,
there is a distinguished timelike direction at any point. Such a strong
assumption, which is contrary to the spirit of general relativity,
should be mentioned in the paper. Because the exposition is so obscure,
the reader has to dig these things out for himself.

This is the kind of paper which gives conscientious referees
nightmares. If one is lucky, one might spot an obvious error like the
above without investing too much time, but a subtle error buried in 30
pages of dense tensor calculations might take months to find.

Stephen Parrott