On Feb 20, 5:55 pm, Edward Green wrote:
[...]


The Kerr solution isn't a disk though. From my searching, it seems
that the two are unrelated. Can you find a non-Wiki reference?

http://xrl.us/bgic4(Link to books.google.com)

That's what I found. I don't see any evidence that this is related to
Kerr in any way.


if you trust this link shortening service, or else google "neugebauer
meinel disk":

There were lots of references, this was the second.

(The web makes any dweeb look learned).

I'm not sure what you mean by "the solution is not a disk". Of course
the solution isn't a disk -- but it is axial, and has some
characteristic surfaces which resemble oblate spheroids. I would
expect solutions related to a disk to have such surfaces, and the
author did say this was a limiting case (of the Neugebaurer/Meinel
disk).

What I mean by "Kerr is not a disk" is that the solution spans all 3
spatial dimensions and is not a metric describing a planar...anything.
Whereas the Neugebauer/Meiniel solution is, well, a disk of rotating
matter.

The only relation between the two seems to be that the rotating disk
is presumed to collapse into a rotating Kerr hole. Past that, I see no
relationship.


I think Einstein-Cartan theory is very cute in that it not only
sidesteps a lot of the singularity and existence theorems that depend
on the strong energy condition [T_uv U^u U^v 0 iirc] because spin
counteracts positive stress-energy.

You mean that intrinsic angular momentum shows up as "negative mass"?
Does this mean if we had a mass with sufficient intrinsic angular
momentum at the Earth's surface it would float away like a balloon?

No. I specifically do not mean negative mass. The best phrasing I can
think of at the moment is negative energy density.

I did go on to think "negative energy" was probably better ... but
why? Do you want to emphasize this is not the rest mass of anything?

Yes - because negative mass [which I have thought about but haven't
formed a solid opinion of] does not exist whereas negative energy
densities can and do exist in limited circumstances.

If we actually had some stuff with this intensive property, I'm not
sure we could tell the difference.

Depleted vacuum via Casimir effect.


Plus it has the same overall
structure as classical GR since you can cast the field equations in a
form that has everything packed into an effective stress-energy
tensor.

With the result surmised above, that it's equivalent to allowing
"negative energy"? How curious that would be.

Yup. That's another reason why I think EC-GR is cute - it's the second
way I know of, other than vacuum energy which is a quantum field
theory thing, to circumvent positive energy conditions.

Well, "mass" or "energy" aside, this naively suggests anti-gravity.

If you have a pure and very large spin source that is massless, maybe.


I'm still not sure I see the relevance of a theory which takes "a
Wessenhoff fluid" as itssource(unless I misunderstood your
remarks). Ordinary rotating massive objects do not resemble
Wessenhoff fluids -- they have angular momentum solely as a result of
the global configuration of many bits of perfectly ordinary matter
moving in a particular configuration.

A Weyssenhoff fluid is a perfect fluid that is _rotating_. It is
simply onesourceamong many that can be put into the field equations,
it's just the most relevant one that I know about. The reason I care
is that when the Weyseenhoff fluid is asourcein the linearized
equations, the metric you get is the weak field Kerr solution. To me
that is tantalizing.

Indeed. All the most interesting areas seem to have clues that are
tantalizing.

Once again - there is no claim about intrinsic angular momentum being
made here. These are bulk properties.

Hmm... on Feb. 13 you wrote:

"Wessenhoff fluid ... is a fluid with intrinsic angular momentum"

Perhaps you didn't mean to put it that way?

I didn't think the wording mattered since I didn't think there'd be
confusion regarding quantum spin. I could have worded it better, I
suppose, but "extrinsic angular momentum" just seems awkward and
simply saying "angular momentum" doesn't seem quite good enough.


I take "intrinsic angular momentum" to mean an intensive quantity
which is integrated over a volume to find a total angular momentum --
similar to a mass density, or a momentum density. We mentioned that
the concept is classically dubious, but perhaps can be rescued by some
vague non-classical effects, in whom all things are possible :-), or
more concretely by a material including distributed microscopic
centers of angular momentum on an unresolved scale - distributed
pointlike sources. I mentioned as a possible example a material with
significant unpaired (qm) spins -- which occasioned a side discussion
how sometimes, when we say "spin" or "spining" we don't mean to invoke
qm; which wasn't essential here anyway, as an example of "distributed
pointlike sources of angular momentum" could be molecules in some
excited state, or even a collection of (classically) spinning pebbles!

The concept of a rotating object isn't classically dubious. The
concept of quantum spin, however, is. Keep in mind that this theory is
still classical.


Provided we don't resolve the pebbles.

The few web references I could find do not really clarify whether
Wessenhoff fluid has "intrinsic angular momentum" in this sense.

http://www.iop.org/EJ/abstract/0264-9381/11/9/017

mentions "self-consistent spinning fluid", which sounds like it may
have nothing to do with intrinsic angular momentum, but also cites
"the ad hoc Wessenhoff spin fluid"! A "spin fluid" sounds much more
exotic than a "spinning fluid", and leaves us in doubt.

http://arxiv.org/ftp/hep-th/papers/0309/0309108.pdf

contains a reference to:

Wessenhoff, J., Raabe, A., "Relativistic Dynamics of Spin-Fluids and
Spin-Particles," Acta Pol., 9
(1947), 8-53

There is a minor discussion of the Weyssenhoff [it has a "y", correct
spelling makes searching easier] in Hehl, et. al, Rev. Mod. Phys., Vol
48, No. 3, 1976 on page 408. If you care about the theory, you should
look it up. If you can't, I'll send you the dozen pages or so I took
photographs of [I lose paper so easily].

There are better discussions he

arXiv:gr-qc/0601089v2 - This is all about the Weyssenhoff fluid.
arXiv:gr-qc/9309027v1 - This is a survey of Einstein-Cartan theory.
Same basic content as Hehl, et. al, but slightly different in
presentation and certain subjective naming conventions for stuff.
Contains more stuff on the Weyssenhoff fluid.
arXiv:gr-qc/0606062 - Trautman's review of linearized Einstein-Cartan
theory
http://www.numdam.org/numdam-bin/fit...974__21_1_89_0 -
contains the derivation of the linearized Kerr metric using a
Weyseenhoff source.


which means someone must visit a library. But I think the title
suggests something more along the lines I had in mind, and that the
author of the later abstract may have been misleading to describe this
as a "spinning fluid". And besides, why would Wessenhoff get to
attach his name to the stuff, if it were just an ordinary kind of
fluid, gaining angular momentum solely by relative motion of its bulk
parts? :-)

No idea. OTOH, if Maclauren could get the entire Taylor series
consisting of expansions centered around zero just by setting the
expansion point to be zero, it doesn't strike me as /that/ odd.


I mention that AFAIK "bulk property", since you mention it, means
precisely something that is (ideally) distributed in this intensive
way -- in the smallest subdivided bit (as dielectric constant, mass
density, and so forth). You may have intended something else, but for
me the evidence points to a Wessenhoff fluid having "bulk angular
momentum" in just this sense, which is the same thing as "intrinsic
angular momentum" as I understand the term.



...

In the Wikipedia article, I see a parameter "J" in the metric? If
that's the angular momentum, it's built in at the outset.

Where...?

First sentence and third equation of section "Mathematical form".

What article?

Sorry... the one on the Kerr Metric!

Oh. The blurb isn't followed up upon or explained so I'll ignore it as
something irrelevant from the author. I'll pay it more heed if I catch
it written in a paper book.


Well, perhaps you are saying we have "spin" in the quantum mechanical
sense. Even then we really don't have "intrinsic angular momentum" in
the continuum sense, but more like a distribution of rapidly rotating
particles below our level of resolution: whether we have tiny rapidly
spinning (but still classical) dust particles, or quantum particles
possessing angular momenta through quantum spin, doesn't really matter
-- as I've said (too many times by now), if we have a distribution of
such sources, I can see the idea might apply.

There is no intrinsic angular momentum here!

Think bulk properties! Bulk properties!

You had better clarify what you mean by "intrinsic angular momentum"
and "bulk properties", since it is evidently not what I mean.

Expunge all quantum theory from your mind. This is a classical theory,
so if I mention angular momentum I mean good ol' r x p.


I have some parting Big Picture thoughts on how I think this all may
hold together and pan out, or else hold out and pan together, but I'll
save them for now. ;-)

http://iopscience.iop.org/0264-9381/20/13/330/pdf
http://iopscience.iop.org/0264-9381/...ect=iopscience

The Einstein tensor for the most general axially symmetric metric
fills several Maple worksheet pages, is highly nonlinear, and is most
likely unsolvable analytically. So I'm going to be more restrictive
and examine an ellipsoidal symmetry instead, which is what I wanted
originally but didn't think I needed to be that restrictive.