Gravitational collapse

[arfa brane]

How is gravitational collapse related to momentum and pressure?

What's the mainstream view as to the cause of gravitational collapse? Most of the hits you get from google say something like: "once a sufficiently massive star runs out of nuclear fuel, it collapses due to gravity". But how?
Another oft-repeated theme is that nothing can escape such a collapsed body, even light. So all the matter in some sense is 'beyond c', if you see what I mean.

I know (thankyou) that relativistic "mass" can be a misleading concept, it's easier to consider relativistic energy, or relativistic momentum. But isn't gravity a product of momentum?

Or are these questions unreasonable? I mean, considering how ignorant I am, etc . . .

 

[AlexG]

How is gravitational collapse related to momentum and pressure?

What's the mainstream view as to the cause of gravitational collapse? Most of the hits you get from google say something like: "once a sufficiently massive star runs out of nuclear fuel, it collapses due to gravity". But how?
Another oft-repeated theme is that nothing can escape such a collapsed body, even light. So all the matter in some sense is 'beyond c', if you see what I mean.

I know (thankyou) that relativistic "mass" can be a misleading concept, it's easier to consider relativistic energy, or relativistic momentum. But isn't gravity a product of momentum?

Or are these questions unreasonable? I mean, considering how ignorant I am, etc . . .

Stars are in a state of dynamic equilibrium between the force of gravity shrinking the star, and the force of nuclear fusion expanding outward. Get rid of that outward force, and there's nothing to stop the star from collapsing in on itself due to gravity. With a star like the sun, it ends up as a white dwarf star. If the star is massive enough to begin with it can trigger a supernova and, if big enough, can continue to collapse into a BH.

Another oft-repeated theme is that nothing can escape such a collapsed body, even light. So all the matter in some sense is 'beyond c', if you see what I mean.

No, its not arfa. It means the escape velocity of the Black Hole is c, and since nothing can reach c, nothing can escape.

 

[brucep]

How is gravitational collapse related to momentum and pressure?

What's the mainstream view as to the cause of gravitational collapse? Most of the hits you get from google say something like: "once a sufficiently massive star runs out of nuclear fuel, it collapses due to gravity". But how?
Another oft-repeated theme is that nothing can escape such a collapsed body, even light. So all the matter in some sense is 'beyond c', if you see what I mean.

I know (thankyou) that relativistic "mass" can be a misleading concept, it's easier to consider relativistic energy, or relativistic momentum. But isn't gravity a product of momentum?

Or are these questions unreasonable? I mean, considering how ignorant I am, etc . . .

The physics which explain whether gravitational collapse ends in stable objects like dwarf and neutron stars or black holes is the 'Pauli Exclusion Principle' [Wolfgang Pauli]. Really interesting physics.

 

[arfa brane]

No, its not arfa. It means the escape velocity of the Black Hole is c, and since nothing can reach c, nothing can escape.

"Nothing" I presume means "no matter inside the event horizon". So, in some sense, the matter inside the event horizon is beyond c.
Or otherwise why does matter need to have an escape velocity > c?

 

[arfa brane]

The physics which explain whether gravitational collapse ends in stable objects like dwarf and neutron stars or black holes is the 'Pauli Exclusion Principle'

Ok, isn't the exclusion principle also known as 'Fermi pressure'? The Chandresakar limit is where gravity overcomes this pressure?

 

[AlexG]

Arfa, you're just playing with words. Matter needs to have an escape velocity > c because that's how strong the gravitational field is at the event horizon. Just as in order to escape from earth's gravity you have to be going faster than 25,000 mph, to escape from the Black Holes gravity you have to be going faster than 182,272 mps, which can't be done.

 

[arfa brane]

Matter needs to have an escape velocity > c because that's how strong the gravitational field is at the event horizon.

Ok, but that only shifts the "play on words" doesn't it? Furthermore, how does it explain the "cause" of collapse?

 

[AlexG]

No, because the words I've used have meaning in this context, and the words you've used don't.

Furthermore, read post #2.

 

[arfa brane]

Let's try again:
How is gravitational collapse related to momentum and pressure?
A: It isn't related to either.
B: Noone knows.
C: What? You expect a science forum to give you free lessons?

Note how the question is asking about collapse, not about escape velocity or a gravitational field.

 

[AlexG]

Let me repost it.

Stars are in a state of dynamic equilibrium between the force of gravity shrinking the star, and the force of nuclear fusion expanding outward. Get rid of that outward force, and there's nothing to stop the star from collapsing in on itself due to gravity. With a star like the sun, it ends up as a white dwarf star. If the star is massive enough to begin with it can trigger a supernova and, if big enough, can continue to collapse into a BH.

Note how the answer is about collapse.

 

[arfa brane]

Stars are in a state of dynamic equilibrium between the force of gravity shrinking the star, and the force of nuclear fusion expanding outward.

But pressure is force per unit area. Doesn't what you're saying mean that, for a given surface area, a massive body is stable if the inward and outward pressure are in equilibrium?

Note how the answer is about collapse.

Yes, you're saying gravitational collapse is caused by gravity. This isn't really an answer.
What about Fermi pressure? What about gravity itself in terms of pressure/momentum?

 

[AlexG]

Doesn't what you're saying mean that, for a given surface area, a massive body is stable if the inward and outward pressure are in equilibrium?

Not surface area, volume, otherwise yes.

Yes, you're saying gravitational collapse is caused by gravity. This isn't really an answer.

Yes, it is an answer. What is it that you don't understand. What besides gravity would cause gravitational collapse?

When the collapsing mass is large enough, gravity overcomes Fermi pressure.

 

[arfa brane]

Yes, it is an answer.

But not much of an answer.

When the collapsing mass is large enough, gravity overcomes Fermi pressure.

Yes that's true. Does that not suggest that gravity is also pressure, or something like "pressure causes gravity"?

Plus, you've mentioned forces, pressure is force per unit area. But GR doesn't have forces. So why isn't there a problem with my question about pressure, as your answer isn't problematic (at least as far as you are concerned)?

 

[AlexG]

Yes that's true. Does that not suggest that gravity is also pressure, or something like "pressure causes gravity"?

No, it doesn't. It suggests that gravity can cause pressure. That's quite different from being caused by pressure, or being pressure. The piston in an air compressor causes pressure, but that doesn't mean that the piston is pressure.

 

[arfa brane]

Ok, can you point to the big mistake in the following?

Gravitational Collapse

Another remarkable feature of Einstein's equation is the pressure term: it says that not only energy density but also pressure causes gravitational attraction. This may seem to violate our intuition that pressure makes matter want to expand! Here, however, we are talking about gravitational effects of pressure, which are undetectably small in everyday circumstances.

 

[jermy]

Ok...first of all it is related to astrophysics,it is related to internal pressure of the star..
The inward fall of a body due to the influence of its own gravity.for any stable body, this gravitational force is counterbalanced by the internal pressure of the body, in the opposite direction to the force of gravity.Obviously, if the internal forces are more stronger than external forces.The mass will start falling inside due to gravity.

 

[OnlyMe]

Ok, can you point to the big mistake in the following?

arfa, where does that come from?

 

[arfa brane]

http://math.ucr.edu/home/baez/einstein/node6.html;
We also have:

Within the star, on the other hand, the metric does depend on the pressure (as I recall this is why gravitational collapse becomes inevitable beyond a certain critical mass, because it leads to a runaway feedback: the higher pressure causes more gravity which causes more pressure which causes more gravity which causes more...). Information about the internal pressure just doesn't escape the star.

http://www.sciforums.com/showthread.php?107377-Does-pressure-cause-gravity/page2

 

[Robittybob1]

When the star is burning and it hasn't yet collapsed there is a lot more mass in the star than there will be in the black hole in the final state. But the black hole is a lot of mass within a certain amount of radius. It is the ratio of mass to radius that causes a black hole not just the amount of mass in an object.
That is my understanding at the moment, so some of the material blasted out by the supernova will escape the black hole for it has sufficient velocity to do this. But there is enough material within a certain radius that can't escape, and much more material just outside that radius that will be fall back down because it had not attained escape velocity.

 

[arfa brane]

It is the ratio of mass to radius that causes a black hole not just the amount of mass in an object.

Yes, every gravitating mass has a limiting radius--the Schwarzschild radius--below which the 'mass density' becomes infinite.

The one you're on the surface of for instance--the planet earth--has such a radius.
A supernova is one way a massive star can form a black hole. What I'm interested in is the process of collapse, in particular, I'm interested in Einstein's objection in which he claims that black holes cannot form. Apparently Oppenheimer and his student were unaware of it and managed to formulate a working model anyway.