Singularities should not be possible.

Matter is energy. Any energy in any volume will create an energy density, which is pressure. This internal pressure times the area of a particle on the surface of a body will create a force directed outward. The gravitational attraction between the particle and the body will also create a force directed inward. But because the internal pressure is inversely proportional to the cube of the radius, while gravity is only inversely proportional to the square of the radius, the internal forces will always increase much more rapidly than the gravitational forces upon collapse, and will counterbalance gravity at some point.

Are you talking about physical singularities or coordinate singularities?

What equations of state and what equations did you use to come to this conclusion?

And how do your EOS calculations and equations differ from the EOS calculations and equations (see appendix A and B) here?

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

I could not refer to the site you posted for some reason or another. The singularity I am speaking of is the same for that proposed for the Big Bang and black holes. The equations are simple. If a body must be squeezed down to zero dimensions in order to produce a singularity, then its boundary must have a zero radius. We can therefore find the relationship between the body and that of a particle that exists on this boundary to see if it is possible to squeeze the body down indefinitely. The total energy of the body divided by its volume gives us the energy density, which is the internal pressure. Multiplying this by the area of a particle on its surface gives us a force pushing outward, or F=[E_body/(4pi/3)R³]A_part. The gravity between the body and the particle will also create a force directed inward, or F=GM_bodyM_part/R². But the outward force is inversely proportional to the cube of the radius while the gravitational force is only proportional to the square of the distance, so that it increases much more rapidly for a smaller radius. If the body were to decrease in size ten-fold, the gravitational force would increase by one hundred, but the internal pressure increases by a thousand.

I know that some of you might argue that the area of the particle would also decrease in proportion, so that the outward force would be much smaller. This is debatable and I would like to hear your comments. It is my contention that the areas of particles is what determines the gravitational force as well, so if the areas of particles were to decrease, then the gravitational force would decrease along with it.

It is also said that a singularity might create such anomalies as wormholes. Even if it were possible to create a singularity, how one gets a wormhole from this I don't know. If one likes the idea of sliding through space and time in wormholes like waterslides at the funpark, then far be it from me to spoil the excitement. Go ahead, have fun with it. But if one wishes to deal with real concepts of science, with real consequences and conclusions, then I'm sorry. The ride is closed.

What really needs to be defined here, is if you are talking about a stellar singularity (black hole), or a Super Massive Black Hole singularity. There is a huge difference!

What you are saying 'might' apply to a stellar black hole singularity. Tim Thompson indicated that there was a solution for a stellar balck hole where the singularity was actually the accretion disc, at least I think I remember that correctly.

Think about this...we know where the mass comes from for the stellar black hole, right? The 'mass' of the star determines the 'mass' or GRAVITY of the black hole. Where does the 'mass', in other words, GRAVITY come from to make a 2 billion sol mass of a SMBH???

[The total energy of the body divided by its volume gives us the energy density, which is the internal pressure]

This assumption is definitely a problem for a SMBH and the singularity within!

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RussT
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Everything is, as it should be, otherwise, it wouldn't be!

AFAIK, all such singularities are idealisations, and come with the explicit or implicit caveat that there is no quantum theory of gravity (or theory of quantum gravity) that has passed any unique observational or experimental tests.

Putting this another way, the physical regimes in which quantum theory and GR are so strongly mutually incompatible as to render any statements about the nature of stuff in them quite meaningless are well known, and such regimes 'occur' long, long 'before' any singularities are reached.Which seems to be a pure GR approach; if you use 'realistic' values and plug in quantum theory (e.g. particle physics Standard Model) inputs, I suspect that these last few sentences would read very differently.Surely the most beautiful, elegant, brilliant, simple, .... theory is only as good as its ability to match good observational and experimental results?

If so, then as (AFAIK) no one has done any experimenting or observing inside a BH's event horizon (or at least they haven't been able to communicate the results of such to us), or during the first ~10^-43 seconds of the universe's existence (etc), all this beautiful theorising is equivalent, scientifically, to speculation, isn't it?

OTOH, if someone comes up with a theory that has consequences that are observationally/experimentally testable (even if only in principle), then we're into a whole new ball-game, right?

There is something troubling about the idea of applying a theory or a set of theories to any specific time after an earlier specific time that cannot be observed. Can a theory validly claim to say that there is a set of conditions that apply, say, 100 Planck times later than 1 Planck time, without invoking the first Planck time? How do the "100 Planck time" conditions manage to ignore the first Planck time?

Could a few other readers check on the link. I'm having no problems.


You do know that the singularities for the BB and black holes have different properties, right? You are also aware that the singularities are nothing more than where the equations break down and become unusable, right?

To make this statement, you obviously have not looked into neutron star equations of states.

Well, not quite, the equations of GR fail once you get down to the Planck length, before r=0.

I don't see an adiabatic index, polytropic constant or pressure gradient in your equations. What metric are you using for the calculations in GR, to show that a singularity is not possible in GR? What fluid velocity and vortex velocity would be used for rotating stars?

That is your contention, you have yet to show how your idea produces Keplearian Orbits or if it matches observations on the binary inspiral.

My biggest comment is that you are not using the correct equations. This idea of yours sounds as if it is a combination of some college physics and popular science simplifications of General Relativity. It does not sound like the idea has been fleshed out, using the correct physics or equations.
This paper give you an overview of EOS equations and their solutions.
What do you propose is incorrect about these equations, that we should use the equations you posted instead

This site models rotating neutron stars.

If you don’t know how one gets wormholes, or how they are created and held open, how do you know it’s not a real concept?

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

In what way are you claiming a huge difference, for the "singularities"? Both result from an infinite curvature. How eaxactly, when mathematically describing their properties, do you claim this?

I think you rember it incorrectly. Please go back and read what he wrote and link to it, so we know what you claim he said is correct.

It comes from 2 billion solar masses of stress-energy.

Please show mathematically why you think so. Please look at my answer to grav, and let us know if you think it is correct, in terms of the Equations of State.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Yes, if only because the full statement comes with all the caveats that are appropriate (which, it goes without saying, are almost never included in popsci accounts).

IMHO, the best you can ask of good theories is that they are internally consistent, consistent with other (good) theories where their domains of applicability overlap, and consistent with (all, good, relevant) observational and experimental results.

From there, you can say "IF {theory} applies in {domain you are interested in}, THEN {conclusions}."

That conditions may have been different 'before' is not at all unusual in science, and (mostly) irrelevant. For example, you don't need to know how the universe began to test the validity of the (economic) theory of comparative advantage, or Darwin's theory of evolution (as it applies to life on Earth).

It's a 23 page PDF, and the link works fine for me.

I've noticed that sometimes links to PDFs cause Firefox to hang (so I've learned to sacrifice IE for these purposes), and that they can be very, very slow loading if you're on a low bandwidth connection.

Perhaps you could right-click on "Save Link As" (or whatever your browser says)?

Thank you, Nereid. it worked that time when I saved it. The document seems rather long and complicated, however, so it may be some time before I complete it. In the meantime, let me throw these thoughts at you all. First of all, it would indeed be very difficult to speculate on the workings of an environment in which we cannot even see past the event horizon. But isn't the main concept of a black hole really only that light cannot escape its confines? Granted that would provide room for some strange effects within its boundaries, effects that may not agree with everyday experience, but shouldn't most of our physical laws still apply to much the same degree as outside. For instance, if a star were to suddenly collapse into a black hole, its gravity outside of the event horizon shouldn't change at all. Just because we can't "see" what is going on doesn't mean that it is anything so extraordinary that we should abandon our laws or even common sense.

It is speculated that the laws of physics might change dramatically within a black hole, so that even space and time are influenced. But time is a man-made concept, used as a constant of proportionality for change. It is simply a comparison of the rate of change of one event to another very stable and reliable frame of reference, such as the rotation of the Earth or a clock. We must follow this ideal definition as precisely as possible for it to be of any use to us. Therefore, time cannot slow down or speed up, go backwards, or sideways to alternate universes, or upside-down.

Space has only three dimensions as it is defined. This is by the minimum number of lines necessary to identify the position of a specific point from a point of origin, which comes to three when they are directed perpendicularly to each other. It can be said to be two when it comes to a surface, such as the surface of the Earth, requiring only a longitude and a latitude. But this is an illusion. One of the dimensions has already been identified, stretching from the north pole to the south pole as an additional frame of reference, or "line" of origin, which is the Prime Meridian, and from this the longitude stems. Even a sheet of paper has three dimensions, but one of the dimensions is constant and irrelevant, so that we only consider the other two. But if we were to bend this sheet of paper in any way, or to curve it upon itself, then we must further consider the definition of this curve, and give it back its third dimension. So to consider that two far away points can be made to exist in the same place at the same time by the curvature of space, as in the case of wormholes, is ludicrous. It is but a parlor trick.

If the universe began as a singularity, then it must necessarily exist within another universe of greater spatial dimensions than what we know. What then, of singularities within our own universe? Would they then lead to lesser dimensions?

You are exactly correct, this is ludicrous!!! Because this is one of the SCI-FI
attempts to try and use a worm hole for something other than it was intended!!!

Just like your treatment of time above, "ALL" the Sci-Fi HAS to be taken out of these discussions, if we are to figure out how GR really does apply to the physical workings of our universe!!!

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RussT
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Everything is, as it should be, otherwise, it wouldn't be!

Quote:
Originally Posted by RussT
What you are saying 'might' apply to a stellar black hole singularity. Tim Thompson indicated that there was a solution for a stellar balck hole where the singularity was actually the accretion disc, at least I think I remember that correctly.]

Ah, here it is Tensor. You were right, it wasn't exactly correct.


Here is his entire post concerning Singularities...
why math?

The real problem here, ladies and gentlemen, is that the T=0 singularity is only a "PROPOSED", "POSSIBLE" singularity, where-as you Guru GR specialists have now determined that the SMBH and it's singularity "actually exists". That is a tremendous human achievement!!!

Now there are 2 keys to understanding the rest of this. The first is to understand that the singularity in the SMBH, DOES NOT suffer the same
10 ^-43 failure as the cosmic one, because it is not trying to start the universe!!! In fact, it can be, and has been modeled all the way to, and through the singularity!!! From the outside going into the SMBH...
accretion disc/event horizon/black hole/ring singularity/worm hole/white hole

That is the absolute beauty and elegance that the maths of Einstein's General Theory of Relativity, when applied correctly, physically descibe part of the processes of our universe! And yes, Nereid, I do mean physically!

Now, a really astute, intuitive GR learned person, might have figured out, that ALL GR singualrities MUST be affiliated with a black hole, and since it has been definitely determined that our universe is not "IN" a black hole, therefore the PROPOSED singularity could not exist, therefore there is no 10 ^-43. Then they may go one step further, and realize that since the proposed singularity had modeled the nucleosynthesis so well, that maybe, just maybe, the "REAL" singularity, you know, the one in the SMBH, could be modeled to do exactly the same thing!

The key to this is understanding a couple of defintions that have been slightly misunderstood. One of those is Tim's use of Infinite Curvature...in the SMBH it is the tendancy toward infinite curvature, but it doesn't go all the way to infinity, otherwise they couldn't have modeled the "Ring Singualrity", right Tensor?
The other defintion that needs to be understood, is "White Hole". There are two, which has been one of the reasons, that this whole concept has remained so SCI-FI, but once you UNDERSTAND each one seperately, it truly does apply physically to our universe!!!

To See How This Can Be, since this is straight GR, Go To Astronomy>"The Birth Of A GAlaxy"

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RussT
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Everything is, as it should be, otherwise, it wouldn't be!

It didn't sound like something Tim would say.

NO, it is not. The equations are unequivocal. The equations of GR fail inside all black holes, at r=0. The name for where the equations fail is call a singularity. There is nothing more to a singularity.

There is a lot more keys to understanding this than 2. There is calculus, there is linear algegbra, there is differential geometry, and throw in a bit of topology with it, just for fun. None of which I have seen from you yet.


It doesn't matter which one, they both fail at distances less than the Planck length. GR does not work at distances of less than the Planck length, so we can say nothing of what happens there. This has been explain to you many times. What about it don't you get?

No, someone who understands GR would know that not all are. Could you point me to the equations that show all singularities have to be inside a black hole? It's a shame you can't use adobe, this site list several different kinds, not all are associated wtih a black hole.

OK, what happens when you try to model something at a length smaller than that. What do the equations show? I ask this since you seem to think that the equations will work, by claiming the singularity doesn't exist.

This above statements are a classic case of what happens when you don't understand the theory. First off, the BB singularity is of a different type from black hole singularities. At the BB singularity, all world lines in GR start there. In a black hole (size doesn't matter), all world lines end. Second, nucleosynthesis has nothing to do with the singularity. It occurs at lengths greater than the Planck length. Please provide the math for the model of SMBH where all matter doesn't fall into singularity.

Wrong. Please point out, how the equations don't fail at a black hole singularity, whether it is a point or a ring. The ring is an artifact of taking the angular momentum of a black hole into account.

Which is interesting, because I have yet to see anything from you that indicates that you understand white holes, any more in depth than popular descriptions (not the math) of white holes. Some of what you propose has nothing to do with GR.

This is about as far from the actual GR equations as you can get. What it is, is nothing more than a misunderstanding, of the general public treatment of GR. You have taken explanations past the point where they are applicable, ignored all the math, and somehow think that this is appropriate, much less possible.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

grav, it's the curvature of spacetime, not just space.
Look here and explain to me just what equations in there are ludicrous or a parlor trick.

Sci Fi? You might want to check with the people who got their Phds working wormholes, and closed timelike curves, within GR. Oh, and Kip Thorne, the Feynman professor of Physics at CIT, did pioneer work with this and has done follow-up work and supervised others working on it. What part of his work and those PhD students is Sci-Fi? And while the application of this requires a level of technology greater than what we have now, (and my not be possible, depending on the timing of the quantum flucuation cut offs) according to theory, it is hardly what I would call Sci-Fi.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Grav is right about a singularity.

A singularity was a simple hypothesis a time ago.
An object above a star has its potential gravitational energy. This potential energy may be transformed in the kinetic energy which alows to go through a star and reach the same potential energy again as previous. It is the energy conservation law.
A Black Hole is a closed energy system. The Black Hole do not allow to lose the energy as it is possible in a radiating star. In the Black Hole all objects exchange the energy between each other. If there is a friction it excites the next objects. The energy can not escape from a Black Hole.

In real Black Hole like object is there more ener