"Steve Bell" wrote in message
...
But the equations are beautiful. I worked up the tensor algebra of the
Kerr
equations of motion (field equations) as linear algebra, for the purpose
of
computation. You can see this representation at:
http://physics.clarku.edu/cip/sbell/suppl.pdf
There is no actual derivation in the above of the Kerr metric, but I
followed very nearly Wald's syntax. It's a fairly quick explanation of to
how get to the computational equations. I must stress, that to a true
GR'ist, I took "license" with issues of coordinate contraction/expansion,
this was mainly to basically get what one would see with our "inertial
brains". I wrote an orbit simulation, "fully Kerr," and generated the
following plots:
http://physics.clarku.edu/cip/sbell/fig1.pdf
http://physics.clarku.edu/cip/sbell/fig2.pdf
It's in FOTRAN, I've been meaning to convert it to C, but for computation
speed on a Windows PC, FORTRAN is just as fast as C. The source code is
available, if you wish. This is for a 10 solar mass black hole (remember,
this is no-where as complicated as n-body) with a test body (the
satellite)
starting off with 0.14c at a 45 deg angle to x-y. The beginning
eccentricity
was 0.5, the reason for the loop-to-loops. With ecc = 0, nice round
circles
are produced, with beautiful deterministic frame-dragging effects bringing
the orbits out-of-plane. A shell can be produced like this. The second pdf
shows how if continued, a torus will be formed. This shows the wide
plasticity of Kerr orbits with their nonlinear frame-dragging effects
(geomagnetism). If GP-B doesn't find this, that would be a blow.
It could be at the birth, very small, almost differential, slight
differences in initial conditions of what-ever-the-hell were the particles
back 13.7 by ago, has by now, produced a gigantic chaotic, but
deterministic, "settling in to some gigantic attractor." The chaos could
have evolved very rapidly (inflation) attaining almost that of today's
complexity in a very small amount of time, and now we are just along for
the
ride. The resolution of this with quantized jumps in the world of the
small
(atoms) is very difficult. But phase space quantized to h_bar will help.
Steve Bell
Here is a Kerr shell about half way to completion. It looks a little
squished due to perspective:
http://sb635.mystarband.net/kerr.pdf
The spherical shell is produced by the Kerr frame-dragging effects. It's
pretty, but I don't believe an actual electron shell is so perfect. I'm
thinking about how to produce a deterministic structure that would actually
look stochastic to the eye.
Steve Bell