Tuesday, May 03, 2005

Lost Horizons

I. Lost Horizons

The Dicke/Yilmaz/Puthoff type exponential SSS metric appears to be incapable of generalization to rotating sources with gravimagnetic fields Hi = g0i, i = 1,2,3 e.g. Kerr vacuum metric in 1916 GR that reduces to the NON-ISOTROPIC SSS Schwarzschild metric when a = J/mc -> 0 where M = 2Gm/c^2.

The Dicke/Yilmaz/Puthoff type exponential ISOTROPIC SSS metric is

ds^2 = -(e^-2M/r)(cdt)^2 + (e^2M/r)[dr^2 + r^2(dtheta^2 + sin^2thetadphi^2)]

Is ALLEGEDLY a solution to

Ruv - (1/2)Rguv = (8piG/c^4)Yilmaz's tuv(VACUUM)

Note, unlike my theory

Yilmaz's tuv(VACUUM) =/= (c^4/8piG)/\zpfguv (Sarfatti)

no one seems to be able to generalize this to the case J =/= 0, where in contrast the Kerr metric of 1916 GR is in the WEAK FIELD limit (for simplicity) is

ds^2 ~ -(1 - 2M/r)(cdt)^2 + (1 + 2M/r)dr^2 + r^2(dtheta^2 + sin^2thetadphi^2)- (4a/r)sin^2theta(rdphi)(cdt)

Where the WEAK gravimagnetic field is the dimensionless weak perturbation

g0phi = -4a/r << 1

There is nothing like this for the Dicke/Yilmaz/Puthoff type exponential ISOTROPIC SSS metric I have seen. Hal Puthoff never sent such a solution.

Also Hal says his metric is good even if M/r -> infinity! (strong field). In contrast, the above 1916 GR metric is only good for r > 2M outside the event horizon that Hal says does not exist. George Chapline in his "dark energy star" theory also says lost horizon, but for a completely different reason.

Note that in orthodox GR MTW epistemology the above metric representations are only for static hovering non-geodesic LNIF observers with non-gravity external forces holding them off-geodesic paths at fixed r, theta, phi.

Note, the full Kerr-Newman 1916 GR metric solution to

Ruv = 0

r outside m & q

with source charge q is, with dimensionless metric tensor components

ds^2 = -[1 - (2Mr - Q^2)/r*^2](cdt)^2 - [(4Mr - 2Q^2)asin^2theta/r*^3](cdt)(r*dphi) + (r*^2/@)dr^2 + r*^2dtheta^2

+ [1 + (a/r)^2 + (2Mr - Q^2)(a/r)^2sin^2theta/r*^2]r^2sin^2thetadphi^2

@ = r^2 - 2Mr + a^2 + Q^2

r*^2 = r^2 - 2Mr + a^2 + Q^2

[Gm^2] = [q^2]

[G^1/2m] = [q]

Q = (G^1/2/c^2)q

[Q] = length


[a] = length

Solar J is 1.63 x 10^48 grams cm^2 sec^-1 (Wheeler & Ciufolini "Gravitation and Inertia" p. 495)

Solar m is 2 x 1033 gm

a(Solar) ~ 10^48/10^33x3x10^10 = (1/3)10^5 cm

2Gm(solar)/c^2 = 0.88 cm

i.e. a >> M for our Sun

That is, if the Sun were to gravitationally collapse keeping fixed J & m it would be a NAKED SINGULARITY without a horizon!

i.e. a < M is the CLASSICAL "Particle" rotating black hole with an outer event horizon where time stops at infinite red shift for outside observer. There is Hawking BB radiation T > 0

The inner and outer horizons for a < M are for

@ = 0

Outer event horizon is

r+ = M + (M^2 - a^2)^1/2

Inner event horizon is

r- = M - (M^2 - a^2)^1/2

a = M is the cutting edge (no Hawking radiation i.e. T = 0)

a > M is a VACUUM ODLRO MACRO-QUANTUM "WAVY" naked singularity - negative temperature for Hawking radiation?

Note that when a > M the horizons have IMAGINARY part that means an extended "antenna" in micro-wave engineering analog problem. See also Alex Burinski's papers.

On May 3, 2005, at 2:52 PM, Jack Sarfatti wrote:

On May 3, 2005, at 2:05 PM, iksnileiz@earthlink.net wrote:

Jack Sarfatti wrote:

No, you are garbling things there.

A&P are working at the level of the antisymmetric torsion tetradic substratum level. The BILINEAR symmetric curved geometrodynamic level is where Alex is working.

Yes, I know.

But Alex is defining alternate connections (metric-compatible LC and metric-free "affine") on a raw manifold,
and allowing the properties of the connection to define the nature of the manifold -- as is typical in modern

I have Alex's GR17 paper in front of me. I cannot understand his physical picture - what he really means by "FR" (Frame of Reference)? I do not see how to relate it to MTW's "LIF" & "LNIF" for which I have a clear and precise measurement epistemology and objective ontology.

Also, I do not understand formally his equation

Riemann Curvature = Affine Curvature - (Torsion + Nonmetricity)Curvature

EEP demands (LC) = 0 in an LIF, since in his model

(LC) = (Affine) - (Torsion + Nonmetricity)

That is

(Affine) = (Torsion + Nonmetricity) in the LIF.

But is this simply an empty tautology like in

F = ma

before one posits a force law like

F_g = GMm/r^2 ?

Alex's torsion is SAME as Shipov's, but totally different from A&P's at the "square root" tetrad level.

Then, very much like A&P, he derives algebraic relationships between alternate connections, such as

LC = A - S

which is very similar to what A&P do with the alternate curvature-free Weitzenboeck connection in their paper.

No, you are completely wrong about that. It's mixing apples & oranges. Severe category error.

That was the point. I thought this comparison would help you to understand Alex's mathematical model.

The relationship between the two levels is NONLINEAR

guv = (Iu^a + Bu^a)(Minkowski)ab(Iv^b + Bv^b)

Bu^a = Bu(Pa/ih)(Vacuum ODLRO Goldstone Phase)

Vacuum ODLRO Goldstone Phase emerges from NON-PERTURBATIVE inflation vacuum phase transition

y = (e^1/x)Step Function (-x)

x < 0 is Spontaneous Breakdown of Vacuum Symmetry causing Inflation.

x = 0 is starting point for perturbation theory, which is no good for this problem.

Yes, of course I realize all this. See above.


On May 2, 2005, at 9:02 PM, iksnileiz@earthlink.net wrote:

Sorry, that's "Arcos & Pereira".

His approach is very similar to that taken in Arcos & Pereirez -- you alternately lay different connections on a raw manifold, and define the mathematical relationships between them. This is what A&P do with their teleparallel Weitzenboeck connection. That is also what Alex does with the "affine connection" A in relation to the LC connection.

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