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GR -> Schwarzschild Metric -> Black Holes
Posted:
Oct 30, 2009 6:26 PM
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On Aug 31, 11:16 am, "hanson" <han...@quick.net> wrote:
> Tom Davidson "tadchem" <tadc...@comcast.net> wrote:
> > From http://en.wikipedia.org/wiki/Sagittarius_A*:[3]
> > "Sagittarius A* has a mass estimated at 4.31 ±0.06 million
> > solar masses Given that this mass is confined inside a
> > 44 million km diameter sphere, this yields a density ten
> > times higher than previous estimates. While, strictly speaking,
> > there are other mass configurations that would explain the
> > measured mass and size, such an arrangement would collapse
> > into a single supermassive black hole on a timescale much
> > shorter than the life of the Milky Way."
>
> So, in reality, there may be no mass in a Black Hole at all...
> ONLY a mathematical reflection/facsimile thereof. Even the
> polar jets and the occasional "feeding frenzy" of a Black Hole
> can be explained by Classical Mechanics of the Barycenter
> as events and effect of the Left or Right Hand rules for the
> former and by collisions of stars or particles for the latter....
>
> It reminds me of D'Alembert and Einstein: "The math says that
> "it" is there, but if you actually go there, then there is no such
> thing to be found and touched"... except in the agile mind of
> Einstein's Dingleberries and mathematicians who do believe
> that the real world does reside within their own mind...
> ahahahaha....
>
> My guess that Black Holes are just n-body manifestations,
> instead of being the exotic specimens that the heuristic paradigm
> believes them to be, it is not a terribly original concept.
> So, does anyone know who has already worked on this
> aspect of the issue?
You are on better track than any self-styled physicists aka Einstein
Dingleberries.
Black holes are predictions from the mathematics of a particular
solution (namely the Schwarzschild metric) to the field equations.
There are infinite such solutions. Please allow me to present the
history once again based on bits and pieces of information with
forensic evidences lying within the very mathematics involved.
During the middle to latter half of the 19th century, Christoffel
recognized that an object moving in curved space might do so in the
shortest possible local distance but not necessarily the shortest as
observed by an outsider. In doing so, he was able to derive the
geodesic equations based on this concept. However, there are two ways
to group the so-called connection coefficients. Christoffel must have
known about the other but chose to publish the more symmetric form now
called the Christoffel symbols of the second kind. These two
groupings of connection coefficients result in the same set of
geodesic equations. However, they are not the same. They are only
the same when the metric is diagonal.
Then, towards the end of the 19th century came this math alchemist
named Ricci. Single handily he invented the Riemannian geometry which
has nothing to do with Riemann. Noticing the geodesic equations can
be written to equation to zero if an operator is able to operate on
the velocity, Ricci the alchemist came up with a mathematical operator
called the covariant derivative out of the Christoffel symbols.
Apparently, he never realized there is another way to group the
connection coefficients. By taking the double covariant derivatives
of two adjacent points in space or spacetime and setting to null, he
also faced with several possibilities in grouping the connect
coefficients. Just like Christoffel, he chose only one and discarded
the rest. His chosen one became what is now called the Riemann
curvature tensor.
The Riemann tensor is actual an n-by-n-by-n-by-n matrix with n^4
elements. It appeared to be a dead end until (I think it was) his
student Levi-Civita came along and invented the Ricci curvature tensor
by contracting the Riemann curvature tensor into an n-by-n matrix with
only n^2 elements.
The nature of the Ricci tensor being cooked out of alchemists? pot
seemed not to have stopped there. It was Nordstrom who realized the
Ricci tensor can somehow mimic the Laplace equation describing
Newtonian gravity in vacuum. The solutions of the Ricci tensor, where
each element describes a partial differential equation, are each
element in the metric.
However, the Ricci tensor cannot satisfy the more general case of the
Poisson equation. It was Hilbert who modified Ricci?s mathematics to
come up with the field equations which include the Ricci tensor itself
plus the so-called trace terms to satisfy the Poisson equation.
Believe it or not. The field equations are never tested. All
predictions are based on Nordstrom?s null Ricci tensor (in vacuum)
since the field equations degenerate into the Ricci tensor in vacuum.
There are actually some subtle mathematical faults leading to the
field equations, but if a diagonal metric is involved such as all test
have done, these mathematical faults become insignificant.
Merely a few months after the publication of the field equations,
Schwarzschild came up with the first solution. After all, he had
several years to play with the null Ricci tensor. So, the feat may
not be as extraordinary as one thinks. Using the linearly rectangular
coordinate system (Euclidean) in curved space or spacetime actually
yields a non-diagonal metric. This would result in ungodly complexity
in the mathematics of solving the null Ricci tensor. However, by
transforming to the common spherically symmetric polar coordinate
system, it allowed him to work with a diagonal metric which would
drastically simplify the mathematics in the null Ricci tensor.
Further reduction in complexity can be achieved by choosing another
set of coordinate system that yields a determinant of -1. So,
methodically did he transform the common spherically symmetric polar
coordinate system into another that would result in much simpler Ricci
tensor thus simpler partial differential equations. Schwarzschild?s
original solution in the transformed coordinate system somewhat
resembled the Schwarzschild metric. However, remember that he had to
transform it back into the common spherically symmetric polar
coordinate system, Schwarzschild?s original solution does not manifest
black holes.
Now, follow the reasoning of the principle of invariance. A geometry
should be something independent of any observers, right? This is the
case because no mortal observer can play God Himself. A segment in
coordinate displacement does not describe the geometry. You have to
specify the metric to do so. Naturally, the metric is going to be
different in each chosen coordinate system to describe the very
invariant same geometry. It is also impossible to tell what the
geometry without identifying what coordinate system is employed. Any
elementary school children should have no trouble understanding the
relationship among the geometry, the coordinate system, and the
metric. However, the saddest part is that the self-styled physicists
do not. Their so-called Riemannian geometry equates the metric with
the geometry and tossed away the coordinate system. That should be
embarrassingly fvcking stupid of them. All but Hilbert understood
what is understood by elementary school children.
A year or two later, it was Hilbert who realized that there are indeed
an infinite solutions to the field equations and presented the
Schwarzschild metric which predicts black holes. Realizing the whole
thing was total crap, he walked away and allowed Einstein the nitwit,
the plagiarist, and the liar to claim full credit. Needless to say
that Einstein the nitwit, the plagiarist, and the liar had absolutely
nothing to do with the nonsense of GR from the very beginning to the
very end. Einstein the nitwit, the plagiarist, and the liar should be
a total embarrassment to science.
On top of that, a black hole predicted by the Schwarzschild metric can
only form in an observer?s very infinite future. Thus, to us, there
should be no black holes formed yet. So, claiming to have identified
black holes is like claiming to see Elvis alive. <shrug>
I am still amazed that the self-styled physicists would collectively
got themselves into such embarrassing mess. Your truly has done
enough work in merely a few years that all the self-styled physicists
combined cannot have done in the past 100 years. The whole thing
about GR is utterly total nonsense. Well, and SR too.
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