On Feb 14, 10:39*pm, Eric Gisse wrote:

On Feb 14, 6:11 pm, Edward Green wrote:

...

There exists a coordinate chart for Kerr that extends past the
horizon. There does not exist, to my knowledge, a solution to the
field equations with some non-vacuum source that has Kerr as the
exterior solution. That's what I meant by "interior".



The vacuum solution inside the event horizon is said to be "unstable" .... or else "unphysical" ...

A Kerr black hole is unstable in the sense that it isn't the "ground
state" of a black hole. The Penrose process for extracting energy is
one reason, and super-radiant instability [nee black hole bomb] is
another. A Kerr hole is very ... obvious in its' environment. It can
impart energy to stuff, and drags stuff along its' direction of
rotation. I personally believe Kerr holes are behind quasars and the
more intense class of gamma ray bursts.

http://arxiv.org/abs/hep-th/0404096

I wouldn't say a flywheel is unstable, though it may run down, but I
would if the flywheel were liable to explode!

OTOH, the author of the wikipedia article goes beyond "unstable" to
"unphysical" ... that sounds like the case where one solution decays
at infinity, and the other blows up -- something that is physically
unreasonable. Of course I don't know what he had in mind.

(although some treatment of a spinning dust disk reduces toKerr
solution in a limiting case).

It isn't a GR solution though - its a solution to linearized Einstein-
Cartan theory. Unless you found something specific to GR, which I'd
encourage you to share.

My sole reference (Wikipedia) mentions the the "Neugebauer/Meinel
disk".

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?

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.

I am tempted to claim that the exterior vacuumKerrsolution, while a
valid solution of the field equations, cannot represent the external
field of a spinning body. As I mentioned, a rotating massive object
seems to transmit no intelligence of its sense of rotation to the GR
source term. If we are in fact able to tell from purely gravitational
observation which way a spheroid is spinning, then there must be some
additional factor which breaks the symmetry.

Thus, Einstein-Cartan theory.

I'm still not sure I see the relevance of a theory which takes "a
Wessenhoff fluid" as its source (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.

...

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".


...

... my objection was that holding the volume
density of angular momentum constant and shrinking the elementary
spinning bits required the angular speed of the bits to blow up.

A fair objection, but one rooted in classical mechanics. You and I
know it isn't that simple.

Classical E&M contains a similar internal inconsistency regarding the
self-energy of an electron.

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.

We might have a role for an intrinsic angular momentum term in a
modified GR, I just don't see how it can have a big role in the
graviational field of objects which are not terribly exotic, like
planets and stars. Maybe neutron stars?

OTOH, I can see the idea might make sense for a system with
significant unpaired spins ...

When I say spin, I do not specifically refer to the quantized angular
momentum of a particle in quantum theory. I treat, in this context,
spin and angular momentum to be the exact same thing. They are as such
in quantum mechanics, but "spin" has a specific connotation that I
don't mean to imply.

I think I read you that way, but we are tripped up by language, since,
when I actually want to talk about qm spin, I have to use the word.
Perhaps we should agree to use "rotating" when we do not specifically
want to invoke the qm concept.

...

At the moment I am satisfied that the Kerr metric is an adequate
description of the exterior metric of a rotating body, Lense-
Thirring effect, geodetic precession, and the observation of near-
extremal Kerr black holes.

So perhaps Kerr stumbled on a physically significant solution of the
GR field equations which cannot be easily justified within the frame
of GR: so the theory is incomplete. But I'm repeating what we've
suggested several time. You suggest the completion is Einstein Cartan
theory; since my understanding of both theories is even more
superficial than yours, but I have my doubts, because of the
appearence of "intrinsic angular momentum". However, maybe the
astronomical objects which seem to be manifesting the external Kerr
solution are really so exotic that this is the right contruction. But
that still leaves ordinary rotating massive bodies out -- unless we
look at the source from so far away that it appears to be a point
source of angular momentum. Maybe that's the trope.