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Reissner-Nordstrom-? metric

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I made one mistake above, as I am just gathering the results I have produced. As one approaches the ring of r=a, z=0, propagation speeds in $\phi$ go through zero at $\rho=2m$ and then approach -1. Propagations in z go as: $\frac {dz} {dx^0}=r/\rho$, and since $\rho$ is going to zero, this blows up in the real range. On the other hand, radially the square root of $1-2m/\rho$ becomes zero, then imaginary, but the total value of interest, the larger fraction, converges on a real negative large value, the inverse of what I thought on 1/2/09, namely -a/2m. Go figure. I certainly am trying to.

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When you consider a polarizable medium like a dielectric, the availability of polarizable dipole moments produces a slowing of the speed of light. Conversely if Nature produces a situation where the SOL is greater than c, it bespeaks a decrease in the available polarizability compared to the usual vacuum $\epsilon_0$. Inversely, a negative response is that of a superconductor, and imaginary parts in the response indicate absorption. If the radial SOL reaches a high, real and negative value I suppose this indicates a weak superconducting response from the vacuum.

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hello, norman -

why does an imaginary part indicate absorption? I understand it from an operator point of view, but could you expound upon that. Further, do you envisage a mapping of a typical superconductor (like YBCO) in terms of polarizability? It might look like the difference of the electron density in a YBCO, w/ the added difficulty of long-range shapes as you back away, above and below, the CuO2 planes...hmmmm

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A usual wave equation reads: $\nabla^2\phi - \frac 1 {c^2} \ddot \phi =0$, and usually $c^2$ is positive. If it is not, then you are faced with: [MATH] -k^2 -\omega^2 =0,, or,, k^2=-\omega^2[/math]. See, something has a real exponential decay now. Also, if you look at EM or even electronics, transverse waves mirror inductance and capacitance, with resistance at right angles to both in the complex plane. . . . . . The methodology in my inhomogeneous electron model (earlier paper) said, let there be an analytically well-behaved charge density cloud constituting the particle nearfield. Charge may be interpreted as a divergence of the electric field; if there is a polarizable medium the accounting may be attributed to the (-) divergence of a polarization field vector. A further step looking at the total field yields up local polarizability, as per dielectric theory.[You too can be way cool with '\ddot' as well as '\nabla'.]. . . . . . . . . .Look up EM equations in a plasma or conducting medium. There is conductivity depending upon responsiveness and density of charge carriers. With electrons there is e/m and so there is a plasma frequency of resonance above which there is a phase shift. Resistance (loss) is quantified at a complex right angle to conductance. . . . . . . . . . I have elucidated a rich cache of phenomenology in GR in the Schwarzschild and the Kerr metrics. There is a fine project in front of me. I read an equation I think by Puthoff that put a scalar polarizability thru the Schroedinger wringer. There should be a richer tensorial relationship to be interpreted here, and I am tuning my dreamcatcher for it. Speak to me in a few... eons. [sorry for my confusion, I will look for that paper.]

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When you consider a polarizable medium like a dielectric, the availability of polarizable dipole moments produces a slowing of the speed of light. Conversely if Nature produces a situation where the SOL is greater than c, it bespeaks a decrease in the available polarizability compared to the usual vacuum $\epsilon_0$. Inversely, a negative response is that of a superconductor, and imaginary parts in the response indicate absorption. If the radial SOL reaches a high, real and negative value I suppose this indicates a weak superconducting response from the vacuum.

Apparently there is evidence from gamma-ray bursters that high energy gamma rays arrive after the low energy ones. One possible explanation is a dispersion effect in the vacuum, that I assume represents a slowing relative to the speed of light. More at this link that we touched upon offline:

http://arxiv.org/abs/0708.2889

Steve

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scalbers can you help me interpret this abstract? Here is the descriptive article you sent, which is useful: http://arstechnica.com/journals/science.ars/2007/08/23/probing-quantum-gravity-with-gamma-ray-bursters . They state clearly that when a large amount of energy (gamma) is in such a small space it is challenging to both QM and GR. What energy range are we speaking of? I wonder if there is a threshold above the 1MEV of e-p production. The theories now deal with the 150 GEV range.

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I can start on that by mentioning tau is the gamma-ray delay in seconds to the galaxy they're studying, in proportion to the gamma-ray energy in GeV. The refractive index is the fractional slowing in the speed of light relative to c. E is the gamma ray energy, though I wonder what M(qg) is - a quantum gravity mass they've somehow derived from the Planck mass?

The PDF file (link in upper right) is a bit more readable for the abstract equations. In the body of the paper, equation (1) helps to spell out the relationships.

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Thanks. I just read the part in Joao Magueijo's book Faster Than the Speed of Light where he describes a somewhat bewildered Einstein working toward the General Theory and making an attempt with a non-constant SOL.

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And by the way in the paper they mention the energy of the gamma-rays runs up to the TeV range.

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My brother sent me Burinskii's paper on the Dirac-- Kerr-Newman electron . Maybe it is time for me to go write music. I have the satisfaction of knowing I got to this level by my own hard work and ignorance. More seriously, only now that I have done this work can I read these papers and hope to enter the discussion.

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I don't yet know enough to say much, but I read things like "extended Dirac spinor field". This is the further "complexification" I was looking for. We are talking $\sigma$'s. HERE: http://arxiv.org/abs/hep-th/0507109v1 This was communicated in 2005 (and '08).

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The Newman-Kerr metric is of rotating, charged mass. Thus it has elements of circular currents . We are all playing the same game, at the different levels offered in Nature.

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• 1 month later...

I should clarify the line in post #54, "Resistance ... at a complex right angle to conductance." I am confusing a couple of things, since we are dealing with conductance either with or without time-dependent loss, and distinctly, with the complex plane comprising inductance, "resistive" flow, and capacitance, where current may or may not be in phase with voltage.

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• 3 weeks later...

I have gotten clear on the analytic properties of the coordinates in which the Kerr GR solution is expressed, vis-a-vis my near-field nullspeed statements. We already knew that $ds^2$ could be negative on spacelike intervals. When you start looking at nullspeeds, or $dx^a/dx^o$ the range goes into the complex-imaginary. This does not mean that the metric tensor does this, and indeed it is real-valued regardless of the coordinate transforms discussed here. It is the multiple, mixed-term entries which begin from the Eddington transform for the time variable, that produce complex solutions in the Kerr. Approaching the singular ring from the outside r=a+, z=0, the value of $g_{oo}$ goes negative, which by itself would demand an imaginary nullspeed. However there are also mixed tensor terms in $g_{01}$ and this makes necessary a quadratic solution and complex expression for radial nullspeed. It might seem at first that this messes up our need for real $ds^2$ but it does not. Following the rules for whichever coordinate system you are in, and adding the complete bilinear sum, consistency follows.

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Norman.. can I now ask you, going back to when I was storngly stating how wrong it is to always use the SR radius instead of an extreme Kerr hole as the correct model for black holes... (well.. tbh.. I do not look at the charge.. but any hole wiht charge must follow from the Kerr hole, rather then the Schwarzchild hole)... do you see more clearly now, through your calculations and considerations, that natural black holes (at least the 'smaller' ones.. i.e. I will leave out SMBH and intermediate ones), are surely Kerr holes rather than Schw. ones and thus.. the event horizon lies on GM/c^2 rather than 2Gm (or 0 and m rather than 2m)?

Or what say you?

lak

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Yah, no, and all the above. I am not analyzing massive things. Yes you speak well of the "outer lotus" . Mass is not much in my considerations. Let the inner lotus open as you allow a system with more Angular Momentum than total energy. I guess life is a polka. So did physicists in the early 1900's. We dance the Planck Polka.

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• 2 weeks later...

I am pursuing the idea of a more fully complexified GR. I do not know yet what to say about the concept of a vector norm whose square is negative. At root, when Kerr solved the angular momentum (AM) problem, he took the simple 1/r solution of Laplace's equation and let z be offset by an imaginary constant. This brilliantly clever move might seem innocuous but it is more than just adding an imaginary constant. Now the expression for radius is: $r= \sqrt{x^2+y^2+(z+ia)^2}$. The kicker comes when you differentiate by z: $\partial r =(z+ia)\partial z/r$. Aha, the spatial differential has a complex coefficient now! This is the sort of system I am trying to formulate.

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In allowing a complex addition to a spatial dimension, like $i\hbar \kappa /c^3$, we let GR cook up angular momentum, in this case on the quantum scale. What might we get doing this to $dx^0$, the time dimension? . . . . .[i use [i]kappa[/i] for grav. const.]

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I made a misstatement and actually wrote the form of the geometric angular momentum, which is the constant a times the geometric mass, or Schwarzschild term: $ma= \kappa J/c^3$ and $m=\kappa M/c^2$. Thus $a=J/Mc$ and the imaginary term is: $i\hbar/Mc$.

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• 3 weeks later...

With some casual Google searching here is a sort of related paper:

Remarks on the issue of time and complex numbers in canonical quantum gravity

http://arxiv.org/abs/gr-qc/9607028

Also this one:

Complex Numbers, Quantum Mechanics and the Beginning of Time

http://arxiv.org/abs/gr-qc/9302002

Then we have this one:

Complex angular momentum in black hole physics and quasinormal modes

http://arxiv.org/abs/gr-qc/0212093

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Very cool, scalbers. The first ref. refers to 'gauge phases' ; the second and third are telling me I'm on the right mathematic track. I have been steadily and slowly advancing on my thesis described more down in the Mathematics Linear Algebra section, of a complete first-order complexification connecting GR and its representation of angular momentum, with quantum theory. http://www.scienceforums.net/forum/showthread.php?p=489040#post489040

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I can no longer be part of this forum.

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That's too bad.. What was the problem? I saw "spam" in the announcement thread... Which doesn't seem accurate...

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• 3 weeks later...

May we live not so long and die out.

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• 1 month later...

Norman has shared with me his solution of a root tensor basis expressed as a sum in equal magnitudes, of the three Pauli spin matrices of a spin 3/2 object. Alexander Burinskii responded with a lively answer as to how these may be quaternions. He prefers a complexification leading to supersymmetry. I personally believe complexification is fine, but a supersymmetry strategy might not necessarily prove fruitful. I LOVE the fact that 1st and 2nd order quadrupolar effects must, by definition, be included, which forces a re-examination of nuclear shell theory and its implications for GR.

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