What causes a star to collapse? (General Relativity)

[OneShotKi11]

Before i start i should state that i am just recently starting to pick up an interest in Physics. Mainly, General and Special Relativity. I will admit ahead of time that i know next to nothing on the subject, but im sure that wont stop anyone from actually answering my question.

Now if i am not mistaken i believe i have just read that Gravity as i knew it does not exist. Infact, it is actually the curvatures of space/time that cause the planets to go round. From my understanding of what i am reading gravity actually does not exist. Is it fair to say that this is a true statement, or do i have a bit more reading to do on the subject?

Well, the reason Black Holes have popped up in my little brain is the fact that i remember reading that black holes are caused/created by collapsing stars. Now what causes the star to collapse, from my (limited) understand is the star not being able to sustain the weight of its own gravity.Allow me to quote something i am reading for a better definition...
"Gravitational collapse begins when a star has depleted its steady sources of nuclear energy and can no longer produce the expansive force, a result of normal gas pressure, that supports the star against the compressive force of its own gravitation."

Now you may already know what im going to ask based on the lead up to the question, but according to what i have learned about General Relativity (Thus Far) i am left with the question...

If gravity doesnt exist as Newton knew it, and its actually the bending of Space/Time, then what exactly will cause the sun to collapse in on itself?
Thus creating a black hole, that will also continue to "suck things in".

Feel free to correct me on anything i might have misinterpreted.
And thanks ahead of time to anyone who answers. Im hoping this thread will develop into an ongoing conversation of the theories and ideas i am just now learning.

Im going to have a ton more questions as time passes!

[CurtC]

Originally Posted by OneShotKi11

Now if i am not mistaken i believe i have just read that Gravity as i knew it does not exist. Infact, it is actually the curvatures of space/time that cause the planets to go round.

Well, that's one way of looking at it, but either way, gravity still exists.

Quote:

If gravity doesnt exist as Newton knew it, and its actually the bending of Space/Time, then what exactly will cause the sun to collapse in on itself?

Gravity. Or the bending of space-time if that's how you want to think of it. Space-time is warped towards the center of the star, and the matter falls down the slope of the warp.

If you really thought that gravity doesn't exist, I'm surprised you're asking about black hole collapse and not the more immediate question of why you're not being flung off into space right now.

[nathan]

Of course gravity exists! It's the mechanism that causes it that was previously not understood. Newtonian gravity theory just said 'mass attracts mass', and offered no explanation about why that might be. There was also an odd coincidence that 'gravitational mass' (how much a given object is attracted to another object) is the same as 'inertial mass' (how much a given object resists changes in momentum). Why are these empirically the same?

General relativity explains gravity as the curvature of space-time. A mental model of that is a warped table with hills and bumps -- but of course to understand that model, we've collapsed space to 2 dimensions, and inserted some 'downward' force to make mass fall down the holes. What GR does is show that the effects we know as gravity can be explained by this curvature and inertial mass -- one of its predictions is that gravitational and inertial mass are identical.

And yes, stars collapse when the inward pressure caused by gravity is greater than the outward pressure caused by stellar fusion, or some other process. For large enough stars the gravitational collapse will overcome the Pauli exclusion principle that allows neutron stars to be one possible end stage of a star -- once that's breached it's all the way to a black hole.

[Skeptic Ginger]

While not proven to exist, neither have gravitons been ruled out.


Regardless of the concept of curved space causing bodies to fall toward other bodies, gravity nonetheless affects the particles within the body as well as between separate bodies.

A star's nuclear fusion counters the gravity until the fusion of protons become too dense to continue fusing. You get elements up to oxygen or 8 protons, IIRC. At that point the fuel is exhausted and no long produces energy which counters the gravitational collapse. Sounds like you understand that part.

So I think your confusion is thinking space ends at the star's edge, and that is not the case.

[Carefulplease]

Originally Posted by OneShotKi11

If gravity doesnt exist as Newton knew it, and its actually the bending of Space/Time, then what exactly will cause the sun to collapse in on itself?
Thus creating a black hole, that will also continue to "suck things in".

Black holes don't quite suck. They just don't spit.

When a star contracts within its own 'Schwarzschild radius', then it effectively becomes a black hole from the point of view of someone free falling through the newly created 'event horizon' created at that radius. However, an external observer never sees the creation of the actual horizon. Because of the ever increasing Doppler shift, it will seem to an external observer that a free falling clock never quite reaches the horizon and that it freezes and slows down to a virtual stop (and you thereby can only 'see' it in a very long-wave radio spectrum). The black hole only 'sucks in' the falling clock, or any other falling mass, in this unhurried manner from the external point of view; although if you dive in yourself behind the clock, then your own radial acceleration cancels the Doppler shift and you see the clock resume its fall, and its normal ticking, as you yourself also pass the event horizon some distance behind it. By the time you pass the event horizon, there is no coming back out.

I assume the black hole is large enough that tidal forces won't tear you apart before you pass the horizon. As for the planetary bodies that were orbiting the former star, they will still follow the same trajectories undisturbed. The external gravitational properties of a black hole are identical to those outside of the star that collapsed into it.

[sol invictus]

There are two basic principles behind general relativity:

1) that matter and energy cause spacetime to curve. The more concentrated the energy, the more the space curves, and it's dynamical - as energy moves around, space bends and ripples in response.

2) small objects follow "geodesics", which are the curved-space analog of straight lines. Given two points, the geodesic that connects them is the shortest path between them (in flat space it's a straight line). In the curved space around a massive object, the geodesics are roughly elliptical orbits that bend towards the object, or in a case with no angular momentum, a radial trajectory falling directly in (which is actually an ellipse too, in a limit).

When a star begins to collapse, it gets denser. As a result the space near it becomes more curved, and the geodesics bend even more strongly towards it. Therefore matter near surface of the star falls in more rapidly, which makes it even denser, which accelerates the process. Unless some other force prevents it, the star's matter will rapidly become so concentrated it forms a black hole horizon.

[sol invictus]

Originally Posted by Carefulplease

Black holes don't quite suck. They just don't spit.

When a star contracts within its own 'Schwarzschild radius', then it effectively becomes a black hole from the point of view of someone free falling through the newly created 'event horizon' created at that radius. However, an external observer never sees the creation of the actual horizon. Because of the ever increasing Doppler shift, it will seem to an external observer that a free falling clock never quite reaches the horizon and that it freezes and slows down to a virtual stop (and you thereby can only 'see' it in a very long-wave radio spectrum). The black hole only 'sucks in' the falling clock, or any other falling mass, in this unhurried manner from the external point of view; although if you dive in yourself behind the clock, then your own radial acceleration cancels the Doppler shift and you see the clock resume its fall, and its normal ticking, as you yourself also pass the event horizon some distance behind it. By the time you pass the event horizon, there is no coming back out.

What would it mean to "see" the event horizon? Event horizons, apart from Hawking radiation, are completely black. You cannot see them. And in fact as matter collapses and the star turns into a hole, you see precisely what you would expect to see - the radiation from the infalling matter gets dimmer and dimmer and dimmer, and eventually becomes to faint to detect even in principle (like when it gets dimmer than the Hawking radiation).

There's a nice sonic analogy for black holes. Suppose there's a river approaching a waterfall. At some point before the falls the current becomes faster than the speed of sound in water. If you're a batfish in that river that "sees" using sonar, that surface where the current breaks the sound barrier is a sound horizon. If you float some little probe in that goes "ping, ping, ping", what you'll hear is "ping, ... piing, ....... piiiiiiiiing, ...". You'll never hear it cross the horizon, and it will appear to "freeze". Black holes aren't really much different (although they are different in some ways, since time is involved in the horizon redshift a more interesting way than it is for the river).

[Carefulplease]

Originally Posted by sol invictus

What would it mean to "see" the event horizon? Event horizons, apart from Hawking radiation, are completely black. You cannot see them. And in fact as matter collapses and the star turns into a hole, you see precisely what you would expect to see - the radiation from the infalling matter gets dimmer and dimmer and dimmer, and eventually becomes to faint to detect even in principle (like when it gets dimmer than the Hawking radiation).

Of course, that's what I meant to convey. You do see objects getting close but never passing the horizon. Even as you follow the falling clock some distance behind, you can never say that you saw it pass the horizon before you also did. That would mean you could still reverse course and be witness of an even that occurred behind the horizon. The best you can do is perform some computations, watch you own wristwatch and deduce that you yourself are passing the horizon... "Now!" (and therefore so must have the other clock that's falling in front of you).

Thanks for the river/waterfall analogy. It's very neat.

[Carefulplease]

Originally Posted by sol invictus

2) small objects follow "geodesics", which are the curved-space analog of straight lines. Given two points, the geodesic that connects them is the shortest path between them (in flat space it's a straight line). In the curved space around a massive object, the geodesics are roughly elliptical orbits that bend towards the object, or in a case with no angular momentum, a radial trajectory falling directly in (which is actually an ellipse too, in a limit).

This explanation is a bit faulty because it leaves unexplained why test masses won't follow similar free fall trajectories with different initial velocities.

Test masses follow 4-dimentional spacetime geodesics. An orbit such as the Earth's orbit around the Sun is the elliptical spatial projections of its 4-dimensional world-line, which is a spacetime geodesics (of the Sun's induced Schwartzschild metric). But an asteroid could have some other 3-dimentional orbit tangential to the earth orbit. It would follow a different orbit if its scalar velocity is different at the tangential intersection point. That's because spacetime curvature, not mere spatial curvature, governs its motion. The orbit varies as a function of scalar velocity because it is thereby the spatial projection of a different 4-dimentional spacetime geodesics.

[sol invictus]

Originally Posted by Carefulplease

This explanation is a bit faulty because it leaves unexplained why test masses won't follow similar free fall trajectories with different initial velocities.

Test masses follow 4-dimentional spacetime geodesics. An orbit such as the Earth's orbit around the Sun is the elliptical spatial projections of its 4-dimensional world-line, which is a spacetime geodesics (of the Sun's induced Schwartzschild metric). But an asteroid could have some other 3-dimentional orbit tangential to the earth orbit. It would follow a different orbit if its scalar velocity is different at the tangential intersection point. That's because spacetime curvature, not mere spatial curvature, governs its motion. The orbit varies as a function of scalar velocity because it is thereby the spatial projection of a different 4-dimentional spacetime geodesics.

You can either specify two (spacetime) points, in which case there is a unique geodesic connecting them (well, usually it's unique), or you can specify one spacetime point and one 4-velocity. Those are equivalent; mathematically you're solving a second order differential equation, so you just need to specify two numbers (per coordinate) to specify the solution.

I chose two points because then I could say that the geodesic is the shortest distance between them. But probably you're right that for orbits, it's more intuitive to specify by initial position and velocity.

As for time, yes, what you say is true. However the difference between spacetime and space isn't so important for the Schwarzschild metric, because the Schwarzschild metric is static (doesn't change with time). That means geodesics have a conserved "energy" associated with time translation invariance, which in turn means you can eliminate time entirely and just specify that "energy" and the spatial points.

[rjh01]

About stars and what happens when they run out of fuel.
A star will burn until it has used too much of its hydrogen. The inner core then contracts. The outer part of the star will expand. The star will then start to burn Helium.

This process will then repeat until the main element left is iron. This element is the lowest energy state of all elements. No matter what element you start with if you generate iron you release energy. If the star is big enough it will then go Nova or even Super Nova. This expels some of the star's mass. This mass will then collide with the dust and generate heavier elements. All elements heavier than iron was formed in this way. Later this mass will form new stars.

Of course what happens depends a lot on the initial size of the star. The first stars were huge giants as they contained no elements heavier than helium. They lived VERY short, but spectacular lives. They then formed the black holes that exist in the middle of the galaxies. The mass they expelled during their very spectacular super novas formed the second generation of stars. These then formed small galaxies. These then combined to form much bigger galaxies.

Stars that are a little too small to produce a black hole produce a neutron star. Most of these rotate very fast and emit pulses of radio waves. These are so predictable that they can be used to navigate between the stars in all four dimensions (including time as the stars slowly slow down). When they were first discovered it was thought that they had discovered ET! What else could emit pulses so regular the biggest error was how good your clock was?

Other stars are called white dwarfs and even black dwarfs. See also main sequence.

The largest stars are red giants. Our sun will one day be a red giant. Then the earth will be in danger of going into the sun.

The above is written from my own general reading. It may contain a few minor errors. If you want to find out more I suggest you do some searches (I have used a few words to help you) or beg, borrow or buy a book on the subject.

[Farsight]

Originally Posted by OneShotKi11

Now if i am not mistaken i believe i have just read that Gravity as i knew it does not exist.

It does exist, but it's maybe not quite what you think it is. It's one of the fundamental forces, but it isn't like the force you exert when you push an object to make it go faster.

Originally Posted by OneShotKi11

Infact, it is actually the curvatures of space/time that cause the planets to go round.

Yes, gravity is known as curved spacetime, but in fact, that isn't really the cause. The cause is the central concentration of stress-energy tied up as the matter of a planet. This "conditions" the surrounding space, altering its properties - Einstein called this g_μv, and causing the curvilinear motion known as curved spacetime. This is what gravity "is".

Originally Posted by OneShotKi11

From my understanding of what i am reading gravity actually does not exist. Is it fair to say that this is a true statement, or do i have a bit more reading to do on the subject?

See above, I'm afraid you need to do a bit more reading.

Originally Posted by OneShotKi11

Well, the reason Black Holes have popped up in my little brain is the fact that i remember reading that black holes are caused/created by collapsing stars. Now what causes the star to collapse, from my (limited) understand is the star not being able to sustain the weight of its own gravity.Allow me to quote something i am reading for a better definition... "Gravitational collapse begins when a star has depleted its steady sources of nuclear energy and can no longer produce the expansive force, a result of normal gas pressure, that supports the star against the compressive force of its own gravitation."

This is right, in that if there wasn't any gravity, a big ball of gas under pressure would just expand outwards. Gravity makes it stay as a ball, then if the pressure drops, the ball gets smaller. This can "go runaway", and you end up with a black hole.

Originally Posted by OneShotKi11

...If gravity doesnt exist as Newton knew it, and its actually the bending of Space/Time, then what exactly will cause the sun to collapse in on itself?

See above. As regards Newton, he had some ideas on gravity that most people don't know about. He said this in the back of his book Opticks:

"Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer?"

He talked about an "aethereal medium" instead of space, and "density" instead of energy density or the stress-energy tensor or g_μv, and he got this density backwards as it happens. But those "curve lines" are essentially curved spacetime. So he wasn't quite as different to Einstein as you might think.

[Carefulplease]

Originally Posted by sol invictus

You can either specify two (spacetime) points, in which case there is a unique geodesic connecting them (well, usually it's unique), or you can specify one spacetime point and one 4-velocity. Those are equivalent; mathematically you're solving a second order differential equation, so you just need to specify two numbers (per coordinate) to specify the solution.

I chose two points because then I could say that the geodesic is the shortest distance between them. But probably you're right that for orbits, it's more intuitive to specify by initial position and velocity.

As for time, yes, what you say is true. However the difference between spacetime and space isn't so important for the Schwarzschild metric, because the Schwarzschild metric is static (doesn't change with time). That means geodesics have a conserved "energy" associated with time translation invariance, which in turn means you can eliminate time entirely and just specify that "energy" and the spatial points.

Yes, I agree. But the geodesics wouldn't be the ellipsis which the orbiting body follows. Rather the ellipsis results from projecting of the geodesics (world-line) followed by the body on the space-like 3-dimentional 'surface' defined by setting t = C (some constant) in Schwarzschild coordinates. (This projection will change a bit over time because of perihelion precession).

[Ziggurat]

Originally Posted by OneShotKi11

Now if i am not mistaken i believe i have just read that Gravity as i knew it does not exist. Infact, it is actually the curvatures of space/time that cause the planets to go round. From my understanding of what i am reading gravity actually does not exist. Is it fair to say that this is a true statement, or do i have a bit more reading to do on the subject?

I suspect you actually misread something. Let me rephrase what might have led you to make this statement.

In GR, gravity is not a force. That doesn't mean it's not real, it just means it doesn't act like forces act.

OK, so what is a force? Well, it's something that causes an acceleration. But, you may object, don't falling objects demonstrate that gravity causes acceleration? Within the context of GR, as it turns out, the answer is no.

Let's take a step back and look at a scenario that doesn't even involve gravity, and is purely Newtonian. Let's look at a ball on a string which you swing around, so that the ball travels in a circle. The string exerts a force on the ball, and the ball experiences a centrifugal acceleration, which makes it go in a circle rather than a straight line like it would prefer to do.

Now suppose we decide to rotate with this ball. We adopt a rotating reference frame in which the ball is stationary. The string still exerts a force inward, but in this frame, there is another "force" which acts outwards, a centrifugal force, which keeps the ball from moving at all. But what causes this force? Well, nothing, except the fact that the ball is not at the center of our reference frame.

In both the rotating and the non-rotating reference frame, the force of the string is the same. But we have this other centrifugal force which exists in the rotating reference frame and not in the non-rotating frame. What's the deal? Well, the deal is that this force is an artifact of having chosen a non-inertial reference frame. It's a "fictitious" force. The equation F=ma applies to inertial reference frames only, but we can make our equations LOOK like F=ma for non-inertial reference frames by introducing fictitious forces. And one of the distinguishing characteristics of all Newtonian fictitious forces is that they are always proportional to mass.

OK, so in the absence of real forces, objects always travel in straight lines. But what if the surface they travel on is curved? Then "straight" doesn't quite apply, but there's an equivalent concept for curved spaces called "geodesic". A geodesic line in Euclidean space is a straight line. A geodesic line on the surface of a sphere is a great circle.

In general relativity, gravity curves space-time. In the absence of force, objects will follow geodesics. But that means they look curved if you try to project them onto 3D Euclidean space. Standing still on the surface of the earth is NOT an inertial reference frame, freefall is inertial. And because standing still on the surface is not inertial, you need to add fictitious forces to your equations of motion if you want them to look like F=ma in this reference frame. And that fictitious force should be proportional to mass, which it is.

But be careful: it's gravity as a force which is fictitious in GR. The curvature is very much real, the curvature IS gravity, and it DOES affect the motion of objects (in a way which we can mimic by treating it like a force) by determining what those geodesic lines are. So gravity is quite real, but it's also very different from forces like electromagnetism. But you can, to first order, treat it as if it were an ordinary force.

Quote:

Well, the reason Black Holes have popped up in my little brain is the fact that i remember reading that black holes are caused/created by collapsing stars. Now what causes the star to collapse, from my (limited) understand is the star not being able to sustain the weight of its own gravity.

Objects on the surface of a massive body want to follow geodesics. Those geodesics would make the object "fall" inwards. They do not follow geodesics because some force (namely, pressure from below) prevents them from doing so. Properly speaking, it isn't a force which makes a star collapse, it's only a force which ever KEEPS one from collapsing. But if the force isn't large enough to prevent collapse, it will.

[Tubbythin]

Originally Posted by rjh01

If the star is big enough it will then go Nova or even Super Nova. This expels some of the star's mass. This mass will then collide with the dust and generate heavier elements. All elements heavier than iron was formed in this way. Later this mass will form new stars.

This bit isn't true. There are a number of processes thought to create elements heavier than iron aside from the r (rapid neutron captrure) process you are referring to. Most notably the s (slow neutron capture) process. The r process is, however, thought to be entirely responsible for creating the elements beyond lead and bismuth.