GarryB wrote:This proper solution does not have the features of the claimed solution by Schwarzchild, Hilbert, et al. The horizon is vanishingly small
around the point mass. So the homogeneous "black hole" solution is actually the case of two distinct space times with one imbedded
in the other. They key detail is that the inner space-time is displacing the outer space-time and not overlapping it. This sort of
material space-time behaviour in the absence of any mass-energy forcing (stress-energy tensor) is one of the innovative features of
general relativity. It is not true that mass-energy is required to tell space-time how to curve. Space-time itself can induce curvature.
Well that makes sense because in effect anything behind an event horizon can no longer be considered as being in this universe, there is a separation between the space time in this universe and the space time inside the black hole, for all we know the rules of space time in this universe might not apply at all, perhaps different rules from another reality of dimension reach through the singularity to the event horizon?
We really need a quantum mechanics consistent theory of gravity before we can talk about he horizon as being a perfect 2D surface cleaving
space into distinct pieces. There has been no success at deriving a quantum gravity theory. We have loop-quantum gravity and super-strings
but we are still far from the end goal.
Clocks do not run faster in gravitational potential wells as the mass
of the gravitating body is increased. They run slower.
Isn't that consistent with the speed of light and issues around dimensional space, mass, and the passage of time?
Time on an accelerating space ship does not slow down because the accelerating spaceship is getting heavier, it slows down because the speed is getting closer to the speed of light.
It would also suggest that black holes are black because the only things that can escape them are 2 dimensional infinitely massive objects for which time in our universe has stopped so they are a non event in space time...
The problem is that Special Relativity confused the subject. It is an unnecessary and wrong theory based on a subjectivist postulate.
1) Maxwell's EM equations are invariant under Lorentz transforms
2) Lorentz transforms were not created by Lorentz but are relevant by virtue of the EM equations having this invariance property.
3) In light of (1) and (2), Galilean relativity is stone cold dead. Inertial frames are deformed by virtue of having a speed.
4) It is only in Galilean relativity where there is no absolute speed limit that transformed inertial coordinates are not deformed
(i.e. the time axis is rotated towards the x-axis, the axis of movement as the frame speed increases).
5) It does not matter what a resident of some moving frame feels. To him/her/it the time axis and the x-axis can
appear to be perpendicular. But to all other observers (i.e. the rest of the universe) he is Lorentz distorted and moving.
Here is the critical failure point of Special Relativity. It asserts that the subjective perception of a frame resident
trumps all other observers and the objective reality that the frame is moving. So we have:
6) In SR a resident of any moving inertial frame always sets his speed to zero and any other frame he sees is supposedly
the application of the Lorentz transform with some abs(v) > 0. Since we do not have any observations that clearly
demonstrate this "every other frame is moving faster than I am" ansatz, we get BS gedanken "experiments" supposedly
proving this viewpoint.
7) It is rather clear that (6) is simply nonsense. In order for the observer to properly map all other frames (which can
be slower, faster or the same speed (direction does not matter) it is an absolute requirement that he know his own
speed. In Galilean relativity one did not care since the frame speed had zero impact on the frame. With the advent
of Maxwell's EM equations we know that this is simply not physical. Frames are distorted by their speed.
8 ) Since (7) no longer allows the v=0 hack, the frame resident will see frames moving faster than he is moving as
exhibiting the usual SR effects: time dilation and length contraction (and failure of simultaneity). But what Einstein
and his gedanken experiments missed is that slower frames (remember that it is only the absolute speed that
counts and not its direction in the Lorentz equations) will appear as time contracted and length dilated (and will
also not have the same simultaneity along their axis of movement).
Summary: All observations attributed to SR are properties of the EM equations which govern our measureable reality since
we are EM constructs. The magnetic field around a wire does not require SR. It requires Lorentz frame distortion. The
same solutions follow regardless of whether the wire is moving faster than the electrons depending on their direction of flow
or the electrons in the wire are moving faster, there is a delta-v between the electrons and the protons in the wire metal
atoms and hence they will not be in the same inertial frame. A good indication that we are on the right path by dropping the
BS (6) ansatz is that all the paradoxes (e.g. Twins, etc.) disappear. They were logical contradictions induced by the
unphysical ansatz (6).
Your intuition is on the right track. Photons know how fast they are moving as there is an absolute rest frame in which they live.
The mere fact that some frame resident is moving does not cleave him off into another reality. The subjectivism afflicting this
field needs to go. Clocks move slower in gravitational potential wells because photons paths are distorted and no longer Eulerian.
The greater the field the stronger the impact. Clocks actually stop at the horizon and any geodesic that touches the horizon
must have local motion at the speed of light. All attempts to fob off the horizon as a "coordinate singularity" are revisionist
Do black holes exist? The above homogeneous solution is possible from the Big Bang. But not from any stellar collapse.
This does not make sense to me.
Surely if anything is going to create one massive black hole it is compressing all the spacetime and matter of the universe into a point smaller than an atom even if it is only for the tiniest fraction of a second...
But then a black hole is not just an enormous amount of matter, it also needs to be highly concentrated into a small area of space time.
Of course one of the other problems is we talk about the fabric of space too much and we start considering it to actually be a fabric, which it isn't. The future expansion of space is described as leading to tears in the fabric of space, which doesn't make sense as space time isn't actually a fabric at all... we just use the term to describe something we still really don't understand properly.
People are not free to abuse mathematics because of some supposed physical intuition (about singularities? Really?). The GR equations embody all the
physical axioms of the theory. Solving for the unforced (no mass and energy) case is not solving for any stellar collapse problem. It is not even solving
for the end-point limit. I already linked a paper that properly solves the GR equations for a point mass. This is the general case that includes any (non
rotating and non-charged) black hole singularity. All black holes have finite masses. It is their density that is infinite. This exactly the point mass solution
as given in the Castro paper.
Any actual black solutions look nothing like the peculiar unforced solution being passed off on everybody. There is no finite radius event horizon. In fact,
the event horizon is infinitesimal itself. Allowing for quantum fuziness (i.e. no exact mathematical point but some vanishingly small volume) makes the horizon
the surface of the singularity. The end result of any stellar collapse is a "point" mass which does not involve the crossing of any horizon into a special bubble
space-time and spiraling inward. Sure, get close enough and you can't escape. There is no longer any paradox as to how the gravity which supposedly does not have
a speed faster than light can escape from the bubble enclosed by the horizon.
If we have neutron stars, then we are likely to
have quark stars.
If we have neutron stars where all the electrons have been crushed into protons to form and object consisting of only neutrons because of the enormous gravity, then further increases in mas when the gravity further increases and a quark star is created... is it interesting that you take the qu of quark and replace it with a d and get a dark start of enormous mass and small size and minimal emission of energy or heat.
Hell for all we know the leading edge of space time might have an enormous thick shell of energy and matter that might be dragging space time out with it to expand into the empty void our universe is unfolding into. It might be dark matter because it is too far away to see and now it is moving too fast for us to ever see it.
Space time might be more like a field, where objects in the field effect the field effects on other objects also in the field.
The current orthodoxy is not helping is explore reality. But the good thing is that all of these exciting possibilities are open and the field is
not closed and dead.
A quark solid would have densities much higher than the billion tons per teaspoon of neutron stars. Before invoking an obviously
incorrect framework to claim black holes, we may want to consider that quark solids do not have any glint from photon scattering and
may emit any absorbed radiation at ultra low frequencies that none of our observational systems can detect. If we are dealing with
condensed dark matter objects then for sure they will have no glint and exhibit surface characteristics like those of the event
But what about things even heavier than that... the earth weighs roughly 5.9 x 10^24 kgs, so 5.9 x 10^21 tons... which is a little more than a billion tons per 2cm sized ball.
And what are up and down quarks made of and will further gravity reduce it to that in an even more dense state.
What density of matter requires an escape velocity that approaches the speed of light?
I would expect the tidal forces on any space ship would mean an event horizon is not needed to cause problems because even if you ship could move at a large fraction of the speed of light as it approached a quark star the tidal forces would shred it and render it incapable of powered flight anyway so escape would not be a possible option.
It would only be with very very large black holes where the tidal forces are much less excessive near the event horizon where a ship might pass with out noticing the trouble it is in before getting close to the singularity and being shredded by tidal forces there.
Surely the best argument against quark stars as an alternative to black holes is that they must be immensely hot and therefore not to be confused with black holes...
As of now there are no proper stellar collapse solutions. This is not due to lack of knowledge about super-dense states of matter which cannot be created in a lab.
It is due to a hack solution based on pretending the homogeneous solution emerges (somehow) if the star gets compressed to a critical radius. In light of the Castro solution,
there is no magic bubble which would allow an event horizon to envelop a collapsing star at any stage other than the fully collapsed (point mass) stage. So we
can have all sorts of awesome states of matter compaction. Gluon solids? Or wholly new particles that no accelerator can generate. At some stage we are dealing
with the Planck scale and the quantum foam.
I have the totally wild idea that compressing matter to Planck-like densities results in some pure quantum emissions into the space fabric itself. Instead of just
compacting arbitrarily, the mass of the original star may dissipate in completely new ways (not just photon emissions). This dissipation would affect the dynamics
of the collapse.
As far as the homogeneous solution itself. It may be that the "super-massive black holes" in galaxy interiors are primordial repulsive space-time bubbles formed during
the big bang. These bubbles act as gravitational attractors outside the horizon and would seed galaxy formation.