Naked singularities

[moth]

cool ALMA and SKA are like watching the earth evolve eyes.

[Norman Albers]

Yes, this is part of the excitement of physics these days. I know an undergrad who spoke to the Astronomical Society (her Dad told me) about neutron stars being fermions. This is news to me. Lately I've been tooling along putting GR into the regime of the small, where we understand that quantum spin is the rule. When we deal with the astronomic, we have significant terms for both geometric mass, or Schwarzschild radius, and geometric angular momentum, the length-dimension term proportional to AM of the system.

[scalbers]

cool ALMA and SKA are like watching the earth evolve eyes.

Yes there's a nice video at their website if you click on "Latest Video".

 

http://www.almaobservatory.org/index.php

[moth]

Yes there's a nice video at their website if you click on "Latest Video".

 

http://www.almaobservatory.org/index.php

 

what a machine! the ALMA dishes are so large, agile, and MOBILE it has to be a milestone in several fields.

i've got to go search for info on fermion nature of neutron stars. thanks!

[Norman Albers]

I shall be trying to understand and explain the difference between a dark gray hole and a singularity without horizon. I need Puthoff's paper which I think I have, to be sure I am expressing his formulation of the GR metric.

[Norman Albers]

Yes, awesome to see the high Chilean radio array, thanks scalbers.

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i'm looking at the online version of sci-am(no 'script right now) but i read "But if singularities can be naked, their unpredictability would infect the rest of the universe. " and my mind wandered as i read the next paragraph or so. maybe destroyed is too much,but they should be conspicuous, so it seems like we should "see" them.

 

Yes, the article moves through many scenarios rather quickly, so you are not alone in feeling "your mind wander".

[Norman Albers]

Puthoff's paper starts with essentially the same attitude I quoted in the first post, that it is "comfortable" to use this metric form. I think this is a misleading path, but happily as per the offerings in this thread, we are within reach of observing whether or not large black holes have event horizons. I don't yet know what to say of this metric: the [math]g_{00} [/math] term goes to zero at a finite [math]\rho[/math], but then it comes back to unity. Hmmm... in the Schwarzschild metric, it goes through zero at r=2m, becomes negative as you go inward, and blows up at the singular center.

[Norman Albers]

It would be nice to hear from people knowledgeable in quantum theory, concerning the possible disturbances alluded to in this article, as we integrate ????????? quantum probability amplitudes of some sort I guess, and I am weak here in theoretics.

[Norman Albers]

What I have been investigating lately is the angular momentum singularity for a "small" mass. For stellar events the mass term in the GR equations is much larger (usually) than the AM term. The opposite is true for any particle. There is a ring-like singular solution in GR for an electron at roughly E-13 meters, though it is of very small, namely Schwarzschild, dimension. This is in addition to the center mass singularity as we are accustomed to except this would be at E-57 meters or so. . . not so relevant. I do not yet know the implications of this GR ring.

[kleinwolf]

I found an article saying that the isotropic metric goes into Minkowskian space for r->infinity, and r->0. Is this what you mean in your starting post ?

[Norman Albers]

Whatever you assume for the near-field problem, the metric must be based on the Minkowski flat space in the far, yes. Thanks for noting the behavior as r goes to zero. I am staring at that and not knowing what to say, but I am speaking to the assumptions we make going into this, yah? . . . .OK I think we need to agree on coordinate names. I call the isotropic radial coord. "[math]\rho[/math]" as opposed to the original "r". In the isotropic metric of the first post, as you take [math]\rho[/math] to zero, the coefficient of the time differential goes to unity, but that of the space differentials blows up. So kleinwolf which coordinate are you thinking about?

Edited March 18, 2009 by Norman Albers

[kleinwolf]

I was in fact writing about [math]\rho[\math], the isotropic metric coordinates. In fact, I read an article in arXiv, but seems in some sense wrong, since I doubt more like

 

rho->infty=>ds^2=c^2dt^2-drho^2Minkowskian

rho->0 =>Singular (space coefficient is infty)...BTW : does this mean galilean : ds^2=c^2dt^2-(infty) drho^2 (space is not considered and hence only time is invariant ?)

 

The other question I had was : which is the "real" radius (measured from earth center) : rho (isotropic radial coordinate) or r (schwarzschild radial coordinate) ?

 

In fact should the metric be isotropic ? If we consider the aequivalence principle, the aequivalent speed of the lift has a direction, and lorentz contraction happens only in radial direction.

[Norman Albers]

It seems you are thinking along the same lines I am, and yes that is the behavior in the isotropic coords. What is real? This does depend where you are, at least as observed by others elsewhere. I am trying to extend the usefulness of the externally flat Cartesian coords. by realizing a polarizability tensor. I suspect the use of isotropic coords. is misleading and motivated by the universality of local observations of the SOL. {P.S. Type '/math' and '\rho'.}

[kleinwolf]

Thanks for the syntax reminder. You agree that in cartesian coordinates, if cosmological constant is 0, a solution is Minkowskian. Is this a mystery that the reality of gravitation could depend on the coordinate you choose ?

[Norman Albers]

Well said kleinwolf. The choice of coordinate representation is critical, I think. You allow or disallow certain geometries by setting the real domain of especially the radial coord. We should be able over the next five years to discern black hole event horizons. If we can it is a blow to, say, Puthoff's dark gray hole construction from isotropic coords. I do think his degenerate event horizons share characteristics with particles. The discussion from Joshi comes from the more orthodox Schwarzschild perspective, as he investigates non-uniform possibilities. . . . . . . Do be careful not to combine different discussions, kleinwolf. Since cosmologic effects are long-distance and small in the near, we say that a near-field from a large and/or rotating mass is set in a Minkowski flatspace in the far.

Edited March 23, 2009 by Norman Albers

[Norman Albers]

Coordinate transformations are used to obtain solutions to the Einstein differential system of equations. It is up to us to follow ARIADNE'S THREAD.

[Norman Albers]

A mature approach does find a blending in the "far field" of local density sources, and this we say is the cosmologic spacetime with significant [math]\Lambda[/math].

Edited April 2, 2009 by Norman Albers

[kleinwolf]

If we used the following assumption on the metric through the Ansatz :

 

metric coefficient in spherical coordinates are function of [math](r,\theta)[/math]

 

should we get a metric for a rotating body (BTW I forgot the name of this space-time)

[Norman Albers]

The Kerr metric was solved in 1963. Yes the final form of the metric terms is fully axially symmetric, which is what you are describing, kleinwolf. However these are not the 'external' Cartesian coordinates, and this is the point of my recent paper elucidating the form of the "low mass AM object", or Kerr electron. Also, don't forget the term in mixed coordinate differentials, [math]d\phi dt [/math]. I think this amounts to some sort of "international dateline" <<handwaving>>.

Edited April 2, 2009 by Norman Albers

[kleinwolf]

And if we used elliptic coordinates (2 centers), would this describe the field of a 2-body system, and hence, if solvable, the geodesic would be the solution for a test-mass in a (pseudo-) 3-body problem ?

[Norman Albers]

This is, for this old dog, new tricks. I've not before encountered these representational possibilities. . . . . . . .Looking in Wikipedia, 'tis a cool way to map the plane. I'll hang out with it to get some feel.

Edited April 3, 2009 by Norman Albers

[kleinwolf]

Anyhow 2-body problem is not solvable in GR (since the test mass is not taken into account, but it should curve space-time too)

[Norman Albers]

solidspin is mentioning hyperbolic and elliptic coordinates so you are hot, kleinwolf. He says the former manifests the latter in 3-D... .

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I think my adventurous friend solidspin has folded a spatial dimension into the hyperbolic tangent, which is a coordinate mapping that sort of brings far things near... in the far field it approaches unity.

[kleinwolf]

There are so many coordinates system, that we could put any a priori symmetry conditions :

 

I suppose using ellipsoidal coordinates is maybe describing an ellipsoidal mass

 

but there are also bipolar coordinates, which implies 2 centers of circles, but I don't know exactly which symmetry conditions can be used for this fixed 2-body centers

[Norman Albers]

It may be that if we know how to work with a given coordinate choice in GR, it should yield similar physics as any other. It seems though that choosing a possible form of the solution at the start is what can mathematically limit, or perhaps, illuminate our understanding. If you just look at the axially symmetric form of the Kerr solution, you can feel some satisfaction of geometric understanding, but in what coordinate space? I worked this back into external coordinates and am marvelling at the "faerie ring" singularity. On the other hand if you assume isotropic coordinates are appropriate in massive singularities, you may be missing much. They cannot map inside the event horizon.