Widdekind

oops --

Gravity is generated by energy, not (only) by mass; Newton's equation is really:

Relativistic particles, by definition, have total (Kinetic) energies, far exceeding their rest-mass-energies; relativistic particles are quantum-mechanically "light" particles, having effectively no rest-mass. As such, a relativistically-compact neutron-star (say) is, effectively, a "neutrino-star", composed of effectively-massless particles, whose Kinetic energies are "doing most of their gravitating". While "gluon field failure" may occur, and would then eliminate ~99% of the neutrons' rest-mass(-energies), the relativistic neutrons "would barely notice"; again, their energies-of-motion were already generating the bulk of their gravity effects.

Thus, in the relativistic limit, the RHS (representing gravity) increases, w.r.t. the LHS (representing pressure), as R^-2; as R --> R_S, the RHS exceeds the LHS, and the relativistic, "light", particles implode. Hypothetical "gluon field failure" may occur, but even then, is probably not relevant.

Nucleons are ~10^-15m (=1 fm) across. The gluon-field between the three quarks, in nucleons, accounts for 99% of the mass-energy of the nucleon; "bare naked" quarks only mass ~3-4 MeV. And, the gluon field can be described by a potential energy, which increases linearly, with inter-quark separation distance ®, approximately U = +(1GeV / fm) x r. Ipso facto, if neutronized matter, in a relativistically compact object, were to collapse beyond the neutron-star stage; then gravity would compress the quarks, within the neutrons, together, reducing their separation distances, and so weakening their gluon fields. In effect, gravity would "take over" for the strong force, confining quarks without need for any Strong-Force-gluon-field. Compressing neutronized matter, by a factor of ~100, would reduce the mass-energy of nucleons, by the same factor, i.e. eliminate the gluon-field, reducing total effective mass-energy, down to the raw "bare naked" quarks themselves, whose total combined raw mass-energy is ~10MeV (=0.01GeV).

As a crude semi-Classical calculation, to estimate the effects, of such "gluon field failure", during gravitational collapse, assume hydrostatic equilibrium (one-zone approx.), in a spherically-symmetric object, wherein pressure derived from the quantum-energy (Fermi energy) of compressed particles:

where we have assumed that compression causes gluon-field failure, so reducing mass. Now, the maximum amount of mass eliminable via compression is 99%; the compression factor on the RHS could be as low as ~0.01. The LHS embodies quantum energy resistance to collapse; the RHS embodies gravity force causing collapse. For some number of neutrons N_n, the RHS would still exceed the LHS, even with maximum mass-loss:

Ipso speculato, galaxy-class Super-Massive Black-Holes (SMBH), of millions to billions of solar masses, might be "more compact" than star-class black-holes, which might merely be "super-neutron-stars", whose neutrons have compressed by up to 100x, reducing their masses by the same factor, due to "gluon field failure". Star-class BH might actually collapse, into giant-planet-massed "neutron-Jupiters" (~10-20 M_J). Galaxy-class SMBH might require even more intense physics to explain how they might resist total collapse, to actual singularity. Even so, these speculations suggest, that the original mass of material plunging into galaxy SMBH may have been a hundred times more than their surviving present masses imply, e.g. the original total mass of material, which collapsed into our Milky Way galaxy's central SMBH, may have been a half billion solar masses.

i don't know the answer to your questions. i'll offer what i've worked out:

(1A) Imagine constructing a coordinate grid, of "geodesic Dyson-spheres", in flat space-time.

(1B) Transport a black-hole to the origin

(1C) Spin the black-hole up to maximal rotation rate

(2B) The non-spinning black-hole would not contort the "Dyson spheres"; however, the radial distances between them, as measured by actual physical rulers, would increase, due to the "stretching of space-time 'out' in a hyper-dimensional direction" (the "sagging of the rubber sheet")

(2C) Once spun up, the Kerr black-hole would stretch the "Dyson spheres", both around the polar & azimuthal directions; the azimuthal stretch would exceed the polar stretch, by up to 20%. Thus, the "Dyson spheres" would be stretched out, in all directions, into oblate spheroids. Those azimuthal stretchings could be visualized, as the spinning black-hole centrifugally flinging space-time away from itself, so "widening the throat in the rubber sheet". (Note: space-time does not actually have the consistency of rubber; space-time does not twist or twirl around spinning black-holes; rather space-time co-rotates, like a tornado, or vortex, in a fluid, which can flow past itself, with space-time near to the black-hole frame-dragging more, and co-rotating faster.) The polar stretchings result from the azimuthal, as depicted below:

According to the Kerr metric, there is no stretching, along (coordinate) lines of longitude, at the equator; all of the stretching, along (coordinate) lines of longitude, occurs over the poles. Thus, at the equator, longitudinal "ribs" of the "Dyson (coordinate) spheres" would remain intact; extensional deformation would only occur (increasingly) towards the poles. And, according to the (approximation) formula for the circumference of an ellipse, the stretching around the latitudinal (azimuthal) direction is so much more, than the stretching over the longitudinal (polar) direction, that whilst the effective equatorial radius increases, the effective polar radius decreases (even though the total integrated circumference, around coordinate lines of longitude over the poles, does increase).

numerical method

i employed the Kerr metric, actual physical metric distances, around the spinning black-hole, both over-and-around its poles (dt=dr=dphi=0, theta=0_to_2pi), and around its equator (dt=dr=dtheta=0, phi=0_to_2pi, theta=pi), can be calculated (dl = |ds²|). In all cases, the actual physical circumference-distances measured exceed 2pi*r by some "stretch factor". i employed Wolfram|Alpha: Computational Knowledge Engine to crunch the numbers. Knowing the azimuthal stretch factor, which i assumed was simply the effective equatorial radius stretch factor (r_eq); and the integrated polar/longitudinal circumference (p_pol); i inverted the formula for the circumference of an ellipse (p=f(r_eq,r_pol)), to estimate the effective polar radius (r_pol). According to the approximation formula, near the black-hole, within a couple of R_S, the polar radius is "squashed"; hypothetical "Dyson coordinate spheres" would be flung way out, equatorially, but "stretch down" at poles.

Spherical gas cloud gravitational binding energy

Cloud thermal energy

Hydrostatic equilibrium (one-zone approximation)

Force-bound, energy-un-bound, gas ???

How could a gas be energetically unbound, yet unable to overcome (gravity) forces involved ?? Inexpertly, the HSE force equation is the more stringent.

oops x2

Flat space-time fabric

Imagine a flat two-spatial-dimensional plane (to be the equatorial plane, of a black-hole). Lay out concentric circles ("hoola-hoops in space"); measure their lengths once around; divide by 2pi; define L/2pi = R. Then you label each of those rings with those calculated "R" values.

Schwarzschild space-time fabric

Add the mass to the middle. Viewed imaginatively from a higher-dimensional "hyperspace" perspective, "flat-land" sags in the center. Physically, if you were crawling around on one of those rings (in a space-suit say), labeled "radius = R"; and if you then reached out for the next space ring, labeled (from before the positioning of the mass) with the words "radius = R + 1m"; then you would observe that an actual meter-stick could now be placed in between the two rings, with lots of space to spare. If those rings had been tethered together, along radial rays, with bungee cords; then those bungee cords would have stretched. That is all you would notice, embedded into the curved space-time fabric. From "hyperspace", you could see, that all that extra space in between the rings, and stretch of bungee tethers, was due to each of those rings, being displaced from each other, "down" through an extra hyper-dimension:

Kerr space-time fabric

Now, spin the black-hole up. According to the Kerr solution, now space-time stretches, not only in the radial direction ("can't reach the next ring out"), but also in the azimuthal direction. Those space-rings labeled "radius = R" would be stretched apart; if they, too, were made of flexible "bungee tethers", then they would be observed to stretch out. Anything rigid would be ripped apart. For example, for a maximally-rotating black-hole, the space-ring around the equator of its event horizon, which had been labeled "radius = R_S" before spin-up, would now stretch out by about 25%. That azimuthal distension could be visualized, as the rotating black-hole "spinning out" the space-time around it, as if by a centrifugal-like force. From "hyperspace" perspective, that centrifugal "fling out" would widen the "throat" of the curved space-time fabric by up to about 25%:

Another property of Kerr space-time, is that, in the azimuthal direction (perpendicular to radial rays), light-cones (cdt vs. dl) get "squashed to the side". Traveling towards a maximally-rotating black-hole, along a radial ray, towards its equator, by the time you reach the inner Kerr-radius, both the prograde & retrograde light-trajectories (defining the azimuthal edges of the light-cone from that point in space-time) converge towards a common, prograde, orbit, around the black-hole, at light-speed. And, since all physical world-lines, of massive particles, must lie within their (forward) light-cones, so near rotating black-holes, frame-dragging whips everything into a "prograde at light-speed" orbit.

Putting the pieces together, if you ringed (the equator of) a maximally-rotating black-hole, at its Kerr radius, with a fiber-optic cable; then you would find that that fiber-optic cable had an absolute metric length of 2pi*R_S. And, if you tried to send light pulses, in both directions, around the space ring; then both bunches of photons would actually be whipped around prograde at light-speed. And, if you suddenly removed the mass entirely, then your "Kerr ring" would contract, down to half of its original length. Alternatively, starting from flat-space as above, the space-ring which would wind up girdling the introduced rotating black-hole's inner-most Kerr radius, would be the one, which you had previously (painstakingly) measured, and labeled with the words, "radius = 1/2 x R_S". But, due to the azimuthal stretching of space-time around a rapidly rotating black-hole, after the same was introduced & spun up, that "Kerr ring" would now have an absolute metric length equal to 2pi*R_S. The factor of half implies, that upon spinning up the black-hole, space-rings previously inside of its event horizon, would emerge outwards, as space-time was "flung outwards", and as the "throat" was stretched wider.

Note, that space-time does not "twirl" around a rotating black-hole, as seemingly suggested, by common visualizations, of frame-dragging (which show radial rays twirling around the central object, like a vortex spiraling down a drain). The Kerr solution is a steady-state solution; space-time is not "winding around the black-hole, more & more, like a growing twirl of spaghetti". Instead, space-time spins with the central object, like a bunch of concentric onion shells, shearing past each other, at different angular velocities ("oblate spheroids spinning within oblate spheroids"). Space-time is not being stretched, or expanded, as if it were really a "rubber sheet". Instead, layers of space-time can shear past each other, like a non-viscous fluid. Regions of space-time near to the central object spin around with the same, entrained into its rotations -- the term "frame dragging" seems appropriate; space-time spins around with the central object (but is not stretching as if from fixed anchors, like rubber bands, which would pull back against the spin).

Please ponder a plane single-time "snapshot" slice (2+0D) of spacetime, bisecting the spherical compact object. Draw radial & azimuthal coordinates on the "rubber sheet"; add a relativistically-compact mass; and the sheet sags deep down. Now, spin the mass up, and the "throat" of the space-time fabric twirls around, a little like spaghetti on a fork, via "frame dragging":

According to the Kerr solution, that winding-around of the spatial fabric squeezes the throat down, by (up to) a factor of two. Also, as the originally-radial coordinate lines twirl down the throat towards the compact object, their "winding angle" flattens out. A Kerr black-hole is maximally rotating, when the twirling around of the spatial fabric is so extreme, that the winding angle approaches zero, i.e. an originally radial ray, on approaching towards the object, gets "wrapped around the axel" infinitely many times; the originally-radial ray, down in at the Kerr radius (1/2 Schwarzschild radius) becomes wrapped around the event horizon, without crossing.

If you dropped a rock onto a Kerr-like object, you would not see the object fall straight towards the surface; instead the object would veer off in the direction of spin, and become entrained into a spiraling orbit around the object.

Relativistically-compact objects "trough" the fabric of space-time, i.e. they generate a curvature, into the fabric of space-time, that resembles a "deep grove", in what would otherwise be a flat "sheet" of (x,t) "fabric". Note, that "x" coordinate is a radial-like coordinate, that threads through the center of the spheroidal object, and out the other side, i.e. take the spheroidal object, run a radius all the way through it, from far far away on one side, through to far far away on the other side. In the absence of curvature, that one-spatial-dimension (x) could be represented as a two-space-time-dimensional (x,t) "fabric" of space-time. The mass at the center (x=0) "troughs" that fabric of space-time.

So, what would a rotating compact object do? Inexpertly, i offer that rotation "rolls up" the "troughed groove" that would otherwise "droop down". I.e. start with the "troughed" space-time fabric, and "grab the bottom of the groove", and "roll it up" (a little like a sleeping bag). In the following figure, time runs vaguely "lower right to upper left"; and the space-time fabric "rolls up to the right" representing the counter-clockwise rotation of the object. Again, the "x" coordinate represents a radial trajectory, from far far away, through the equator, and then center of the rotating object (latitude = 0 degrees), and then on back out the equator at the opposite side, and on out to far far the other way. Thus, the compact object would "hang like a bead" on that "x" coordinate line; but the x coordinate line is not polar, but equatorial, so that the "bead" would actually be rotating counter-clockwise (left-handedly). Extracting energy, as by the Penrose process, would involve "un-furling" the spacetime fabric (even as the rotation "furls" the "trough groove" imputed into spacetime, by mass):

Is the above an acceptable way of visualizing (in 1+1D) the curvature effects, of rotating compact objects, that "frame drag" the fabric of space-time?

oops -- i think that's wrong. About their equators, idealized rotating compact objects are symmetric. So, no radius, from the center on out, is distinguishable, from any other. But my drawing above, which tries to tie two radii rays together, shows a qualitative difference, in the curvature, on one side ("curls in and around") vs. the other ("curls the other way"). At best, only half of my drawing could possibly be qualitatively correct -- perhaps one of the radial rays qualitatively captures the gist of curvature, imputed into spacetime, by rotating compact objects. If i had to guess, since rotation acts like "anti-gravity" in the sense of centrifugal forces, so i would guess, that the ray incoming from the RHS in the above figure -- the ray for whom spacetime "furls the other way" -- might be more correct (less wrong). Somehow, all radial rays, from all azimuthal angles, would then "stitch together", for visualizing the fabric of spacetime, near a rotating compact object. (By way of comparison, the Flamm paraboloid for non-rotating BH is generated, by taking the solution for a single radial ray, and sweeping it around 2pi azimuthal radians, i.e. it is a surface-of-revolution; likewise, if any part of the above picture is correct, then one radial ray would have to be swept around 2pi azimuthal radians; every radial ray would be indistinguishable.)

Rock in the elastic regime has a quasi-constant-valued "spring constant". If so, then extension or compression would not affect the elastic properties of the rock. Ergo, no change in pressure-wave propagation (except for density, more/less mass to move in compressed/stretched rock). However, pressure waves could possibly push rock beyond the elastic regime, into plastic / failure regimes. I.e. earthquakes could induce secondary, sympathetic, "copy-cat quakes". (Cp. earth's moon may be able to tidally induce quakes.) So, secondary sympathetic quakes would indicate regions where the rock had been under extreme loads. However, are those spring-constants the same, for both compression / extension? Or, is one spring constant different than the other? If so, the seismic data could possibly discriminate between compressed vs. stretched rock, based upon inferred elastic spring constant? (Perhaps Californians could artificially trigger quakes along the San Andreas, so as to "make small ones", rather than "waiting for the big one", i.e. for pressures to predictably inexorably build, as they are of course, this very moment.)

Primordial nucleosynthesis was not an equilibrium. That's why only light nuclides were produced, instead of just iron. So you can forget all arguments comparing temperature with reaction energy.

 

I suppose the part of the big bang hot enough was too short to achieve any equilibrium - but ask a specialist.

 

 

Fusion from helium to carbon and oxygen does not pass through lithium in stars. There are easier paths.

Fusion happens widely before 2 MeV in stars. 15 MK in a normal yellow star makes 1.3 keV.

First, the number ratio of H:He is approximately 12:1. Triple and quadruple "alpha particle" (He) collisions would have been unlikely. And, in the absence of any accumulated C,O, the catalytic CNO cycle cannot run. Are those the "easier paths" to which you refer?

Second, temperatures after the Big Bang dropped from "super high"; so the word "before" would apply, to higher temperatures, not lower. Perhaps you are suggesting, that fusion could have continued to occur, on down until colder later epochs?

Third, primordial plasma was only "singed", not "burnt", in the sense that >90% of the H remained unfused (thereby remaining for future generations of stars).

Coal deposits from Australia 200-150Mya, when India was adjacent:

Could coal deposits in eastern India, on the following figure, be geologically related??

http://www.interactions.org/sgtw/2005/1026/iow_20051026.html

If rock is stressed (extension, compression), then do seismic waves propagate there-through differently? Can seismic data indicate where rock is being compressed, vs. stretched? Inexpertly, differences in density (compression increases, tension decreases) might be observable

If primordial fusion did happen to occur at ~1MeV; then primordial fusion occurred in a temperature regime not since repeated, by any natural systems. For, even the most massive stars, which burn Silicon into Nickel (which decays into Iron), operate at temperatures <1/2MeV. Thus, if Big Bang fusion occurred at ~1MeV, then Big Bang nucleosynthesis occurred at "supra-natural" temperatures.

http://en.wikipedia.org/wiki/Silicon-burning_process

[math]p^{+} + e^{-} + 1MeV \rightarrow n^0 + \nu_e[/math]

Ergo, when the sum of thermal (KE) energies of the particles on the LHS, can no longer supply the ~1MeV of energy, then the reaction becomes quenched, and the neutron:proton ratio is frozen in. If two particles must supply 1MeV, then the quenching temperature would be about kT~1/2 MeV. At that temperature, the Boltzmann factor e^-E/kT would be about e^-2 ~ 1/7. And the observed n:p ratio is ~1/7. So, again, do not all the seemingly relevant energies point towards a Primordial Nucleosynthesis temperature regime, of ~1/2-2MeV?

Seemingly interestingly, the initial deuterium binding energy (~2MeV) forestalls fusion at higher temperatures. But then the "Lithium hill" (~2MeV per nucleon from He to Li) blocks any fusion that does occur, from hurdling that hill, and fusing on to CNO. Meanwhile, once fusion onsets (~2MeV), neutrons are commonly formed, until ~1/2MeV, so that fusion occurs in a neutron-rich environment. Below ~1/2MeV, neutron (and positron pair) production are quenched. Inexpertly, higher temperatures combined with more neutrons would both reduce Lithium production, bringing theory closer to observations.

Both Jupiter and our Sun evidence differential rotation, with their poles spinning slower, than their equators. (For Jupiter, the difference is ~1%, for Sol, ~30%.) And, at least with Jupiter, the magnetic field rotates with the polar regions. Inexpertly, that implies, that the magnetic field rotates with the core, which is presumably about as big, as the (projection of the) slower-spinning polar regions; and that the core experiences a slowing torque, so progressively spinning down, whilst the equatorial regions swirl on ahead. Inexpertly, that resembles the spin down of pulsars, due to radio emission, from their spinning fields. Perhaps the equations for pulsar spin down apply to stars? If so, then their spinning down can be accounted for, by EM emissions. If not, then other physics are implied. "Skumanich" spindown of stars scales as P ~ t^-1/2.

http://en.wikipedia.org/wiki/Jupiter#Orbit_and_rotation

http://iopscience.iop.org/0004-637X/669/2/1167/fulltext/

The binding energy per nucleon of Lithium is ~2MeV greater than for Helium. And, observations show that Lithium is scarce. Do these facts imply, that when primordial fusion was occurring, the ambient temperature was <2MeV (so that the "energy hill" from Helium to Lithium was not crossable)? The binding energy of Deuterium, the first step for all future fusion, is ~2MeV per nucleon. "Naively", Deuterium would begin to be stable, when the ambient temperature dropped below kT ~ 2MeV. Qualitatively, all the "naive numbers" point to ~2MeV as the relevant temperature value.

Now, 2MeV ~ 20e9 K. And, if primordial fusion occurred at giga-Kelvin temperatures, then allot less Lithium would have been produced. So, would "hot primordial fusion" be able to account, for the scarcity, of Lithium?? The presence of "more neutrons" during primordial fusion would be able to accommodate observations (the .ppt document). And, at giga-Kelvin temperatures, more neutrons, relative to protons, remain stable.

Also, the neutron-proton mass-energy difference is ~1MeV. So, "all the numbers seem to point to the 1-2MeV regime". If so, then neutrons would have been (nearly) as abundant as protons. Could "hot neutron-rich" fusion account for observations??

http://www.astronomy.ohio-state.edu/~dhw/A682/p6.pdf

http://www.astro.rug.nl/~hidding/ao/energy_big.jpg

http://www.ioffe.ru/astro/QC/img/abund_t9_big.gif

insti.physics.sunysb.edu/~meade/phy599/vonhippelslides.pptx

http://phys.org/news/2011-09-cosmic-weight-reveals-black-hole-galaxy.html

The motions of gas around the cited galaxy look like they break down into an outer shell, spinning one way, and an oppositely spinning inner shell

this is an abandoned explanation

of course

because the micro-lensing effect of cold bodies that massive and abundent was searched and not observed.

no -- numerous lensings were observed, whose implications require... theories and models of the galactic halo... none based on... observations. To date, humans on earth have only weak relevant observing capability, and observing data

Geologically, earth is a big rubble-pile of rock in space. Earth has a macroscopic dipolar field; earth is composed largely of iron; iron atoms have microscopic dipolar fields. Parsimoniously, earth's core generates a big dipole field, by the combined efforts, of zillions of iron atoms.

Stars, by contrast, generate more complex fields; perhaps theirs derive from electrical currents?

Again, earth is composed of non-ionic material; non-ionic material generates magnetic fields, from intrinsic quantum dipole moments. All natural magnets known are such. Perhaps earth is "just a big lump of lodestone"? Perhaps the core is a giant ferromagnet, undergoing zone growths, and decays, and thermal heat destabilizes some zones, which then re-establish themselves, only to decay again later... every so often, the entire core is thermally de-magnetized, and it takes awhile for core-sized zones to regrow??

Photons are "proven", by the fact, that faint beams, of high-energy photons, few-and-far between, can still ionize materials (photo-electric effect); whereas below the ionization energy, even intense beams, of low-energy photons, pouring in in dense streams, still fail to ionize materials. Electromagnetic energies do not add, willy-nilly, as in Classical conception. Instead, energy is confined into packets, of quantum-scale energy E=hf. And even infinitely many low-frequency photons cannot ionize materials (having higher ionization energies). You cannot have constructive interference, of zillions of radio frequency photons, produce a "spike", which can ionize a hydrogen atom. Only UV photons of ~14eV or more can do so; and, even if they are the only UV photons for parsecs around.

Now, meanwhile, if you calculate the energy of radio frequency photons; then even low power, 10W ham radios, are streaming out zillions of photons. So the Classical calculations are close-to-correct. Quantum effects are only noticeable, for faint transmissions, consisting of countably small numbers, of individual photons.

Quantum particles of mass-energy, residing in the fabric of space-time, resemble actors, on a stage. The actors can only run across the stage so quickly (speed of light limit); but the stage itself can expand / stretch / grow at any rate. The Hubble Expansion is the latter; the stage is expanding, and carrying the actors (in galactic scale clumps) with the expansion

i know of no cosmological computer simulations, that include the "small" astronomical star-scale effects, of turbulence. Perhaps primordial turbulence could have slammed streams of space-gas together, fast enough to overcome pressure, and so trigger bursts of primordial star formation??

Iron can have magnetization densities of [math]\leq 10^6 A/m[/math]. Ergo, the magnetic moment in earth's core could derive from the spin-magnetic moments, of the vast masses of iron atoms, residing therein:

The OP proposed that charges are separated, in earth's core, with (say) electrons residing in a negatively-charged toroidal belt about the equator of the core; and with (say) holes residing on the rotation axis. That proposed configuration would resemble the 'dz2' electron orbital:

The outer belt of (say) electrons would generate a magnetic field, which would tend to keep the electrons away from the central axis; and which would tend to keep the holes on the axis. Thus, the configuration would be magnetically stable. But, there would be a strong electrical attraction, between the regions of opposite electric charge. Without finagling the numbers, the electrical attraction would be (?) three orders of magnitude greater than the magnetic repulsion. The numbers work out much better for stars, which are larger, and can keep the charges farther apart. Perhaps stars may generate dynamos electrically; but perhaps worlds, composed of non-ionized material, generate dynamos magnetically??

The magnetic potential energy of earth's core is small, compared to the gravitational potential energy, of earth:

For comparison,

Earth's internal natural nuclear fission geo-reactor generates ~45TW of power; the magnetic potential energy of earth's core is about one "earth month" of energy; the world's gravitational potential energy is about a trillion times more, or about a hundred billion "world years" of energy.

Employing the formula for a dipole magnetic field, the field strength, at the surface, at earth's equator is:

where i have assumed, that the charge carriers generating the field, reside in earth's metallic core, near the surface of the same, in a toroidal belt about the equator of the same, carrying a charge per unit length of [math]

\mu[/math] (see below). Ergo

Now, by simple integration, the voltage generated, by a current loop, at the center of the circle, is:

Ergo,

According to this model, earth's dynamo is generated by a quintillion Coulombs of charge, generating ten gigavolts, from surface to center of earth's core.

If charges were separated, into (say) electrons in an equatorial toroidal belt; and holes in the center; then that configuration would be stable. For, the electrons in the outer belt would generate a dipole magnetic field, which would push them outwards, keeping them in place; whilst holes, experiencing oppositely directed magnetic forces, would be pushed back towards the center, keeping them in place. Only if the field got twisted and "fouled up", would charge carriers begin to migrate out of position. But charge separation would be the stable condition. Charge reversals, brought about by turbulence, field failure, and field re-generation, back into the "other" (charge-reversed) stable condition, could account for random field reversals.

Repeating these calculations, for our Sun, would plausibly generate even larger numbers. Approximately, the Sun's rotation period (P) is ~30x longer; and the Sun's core radius is ~30x larger (and is only about ~1/4^th of the Solar radius, instead of ~1/2 as for Earth). Those numbers would reduce the Sun's core voltage, compared to Earth, by a factor of a few (few GV); but increase the charge separation by a factor of 10⁴ (10¹⁹ C).

Employing the online exoplanets.org plotter, i played around, looking for parameters that distinguish Hot Jupiters (HJ) from "normal" planets. HJs hug their central stars; they have small orbital radii, and short orbital periods. So, i used "orbital period" on the X-axis of the plotter. Then i tried various other parameters, for the Y-axis. Inexpertly, one parameter does distinguish HJs from conventional worlds. That parameter is "spin-orbit misalignment" (SOMA). Unlike "normal" worlds, which tend to orbit in the equatorial plane of their host stars, the SOMA of HJs spans the range, from [math]-180^{\circ} < \lambda < +180^{\circ}[/math]. Inexpertly, HJs, and only HJs, tend to orbit spin-tilted stars, often tilted over entirely, like the planet Uranus in our solar system. Is this correct; is my understanding of "SOMA" accurate? If so, why might mis-aligned star spins & world orbits promote planetary migration, until the HJs spiral in, onto star-grazing orbits ?? For example, if the original proto-planetary disk did swirl around the central star's equator; then the HJ-to-be would have punched up through, and then back down through, said disk, every orbit. What might be the effects, of such "disk crossings" ?? Would some sort of "spiral density waves" tug the planet towards the star??

the angle between the stellar spin and the planetary orbit can be measured for transiting planets

 

http://www.exoclimes.com/topics/changing-views-on-spin-orbit-alignment/

http://exoplanets.org/plots

The following figure, from the following article, helpfully visualizes, and emphasizes, that HJs often orbit retrograde (which might make planet migration more likely). Inexpertly, b/c the SOMA of HJ are (apparently) random, roughly half of all HJs orbit (partially) retrograde; and, roughly half of all HJs show signs of "bloating" or "inflation", having planetary radii too "puffed up" for easy explanation. Could retrograde orbits somehow explain HJ inflation??

http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/full_html/2011/03/aa16331-10/F3.html

http://www.aanda.org/articles/aa/full_html/2011/03/aa16331-10/aa16331-10-fig3.jpg

I like the questions you raise and good observations, but when you said 6x as much dark matter as light matter, that is a slight exaggeration. According to Wiki there is 5.25 times as much DM as LM.

 

 

"...its [DM] existence and properties are inferred from its gravitational effects on visible matter, radiation, and the large scale structure of the universe. Dark matter is estimated to constitute 84% of the matter in the universe and 23% of the mass-energy.[2]"

 

http://en.wikipedia.org/wiki/Dark_matter

 

84/23 = 5.25x

 

Does light matter (everything that is not dark matter) include all the invisible gas, dust, black holes, brown dwarfs, invisible planets and moons, and asteroids in the universe?

Everything you suggested would currently be classified as "Dark" Matter.

Now, during star formation, the central stars capture >99% of the material. For example, in our solar system, the mass of all orbiting bodies (worlds, asteroids, comets) is perhaps [math]2 M_{Jupiter} \approx 0.002 M_{\odot}[/math]. So, to claim that the ~5x unseen DM is composed of those "world-like bodies" seems implausible. Conversely, uncritical extrapolation of the stellar initial-mass-function, estimated from astronomical observations, predicts an infinite number, of low-mass brown dwarves; uncritically accepted, DM could plausibly be composed, of dim faint brown dwarf "sub-stars", lurking out in space, not glowing (no core fusion), and so not telegraphing their existences, to humans on earth.

Simplistically, if the "form" of fundamental physical laws survive BC/BB, whilst the constants of proportionality change:

then somehow the "form" of physical laws would be "intrinsic" to the fabric of space-time, like GR says about gravity; and the fabric of space-time would somehow survive BC/BB more or less intact. The minor modification "variations", [math]G \rightarrow G'[/math], would somehow be "superficial", a little like some adjustable pressure setting on a hydraulic system. Through every BC/BB, the forms of fundamental laws would persist ('product of masses over distance squared"); only the "adjustable strengths" of interactions, which strengths are reflected in the fine-structure constant(s), would change ("the new G is 7.76e-12").