Mathematica Black Holes-mathematical singularity or physical reality?

[RoboSapien]

...Elements lighter than iron 'burn' hot enough to support their own weight, iron does not. The only place iron exists in sufficient quantities for this to happen is in the core of extremely massive stars that have used up their supply of fusionable [lighter than iron] fuel in their core. At that point the core rapidly begins to cool until it can no longer support the weight of its iron coffin...

If iron is unable to support its own weight then what is going to stop the fusion of thoes atoms ?

And from where did all other atoms heavier than atoms came from ? Is it fusion ?

And why will the fusion stop at any of the heavy atoms ?

 

[selfAdjoint]

If iron is unable to support its own weight then what is going to stop the fusion of thoes atoms ?

What stops it is that as an element iron is at the bottom of the curve of binding energy. It takes input energy to either fuse an atom of iron to something heavier or to fission it into something lighter. With the elements lighter than iron you get a little more energy out of fusion than you put in, so the fusion can spread, but fusing iron is like rolling a rock uphill.

 

[matt.o]

And from where did all other atoms heavier than atoms came from ? Is it fusion ?

The elements heavier than iron arre formed by fusion in supernova.

 

[SpaceTiger]

The elements heavier than iron arre formed by fusion in supernova.

If you define fusion to be an exothermic reaction, then this isn't quite true. Actually, elements heavier than iron are formed in two ways, the r-process and s-process. The first process does occur in supernova remnants, but it has to do with the bombardment of elements with neutrons. This process is endothermic and requires the extreme temperatures from the supernova remnant to occur. Many elements formed in this way will decay to more stable states, but a lot of neutron-rich isotopes of heavy elements are formed. The s-process also involves neutron bombardment, but it occurs very slowly in massive stars.

 

[Billy T]

Ohwilleke, in post 23, expressed his reasons for thinking that black holes were not dark matter. SpaceTiger noted in post 25 that Ohwilleke argument needed black holes larger than 10^4 solar mass. I like to think most black holes are only a few SMs - cores of long dead stars. I also tend to think there may be more of them now than all the stars currently emitting light. (Many generations of relatively large stars died and left BHs behind long before sun was born etc. Also because many meteors are chunks of iron, and iron not being able to exothermically fuse being the reason for black hole formation by large stellar cores, it seem clear to me that the instablity of the typical collapse is far form symetric. That is, for me it is possible that very big chuncks of iron could separate also during the collapse of a supernova core - perhaps big enough back when allmost all stars were very big compared to the sun, that a few separate, but gravitationally bound BHs could have been created by each supernova - the iron meteors even got away. Admittely not very standard theory (this year any way )

Any comments would be welcome, and BTW, what about the original question Ohwilleke was responding to: Can most of the DM be BHs, especially the few solar mass ones I think must be very common?

 

[RoboSapien]

An explosion that pushes outwards also pushes inwards. And for matter at the very center, how is it going to explode and push its way through the star - there is a star in the way!? Also, the star is collapsing rapidly, so before it explodes it first has to build up enough pressure to halt the collapse. So the reaction gets more and more energetic, the pressure gets higher and higher, and...

And WHAT ?

Your first line here says something about the center pushing outwards, now this is the center and there is no inward, I am lost. If the star collapses in the mean time that's just going to increase the pressure further ?

 

[pervect]

Noooo, I am an amature but that's not what I meant to ask. Please try to understand. I mean when the star is about to explode the pressure at the center must be immense and hence fusion will start there first as the fusion starts that will add more pressure in the center and hence star should begin to explode from the center leaving nothing to form a black hole.

I know I am wrong but how ?

Let's see if I can explain.

The fusion in a star occurs mostly at the center. The fusion process generates a lot of heat. The heat is what keeps the outer layers of the star from collapsing.

When a star runs out of hydrogen to burn, it turns into a red giant. Take a look around at some web pages for more info on this process, such as

the wikipedia

The center of a red giant is actually hotter than that of a star that burns hydrogen - it has to be hotter, in order that helium will burn. But, paradoxically, because the center is so hot, the rest of the star expands.

Note that there is a very important relationship here - internal heat causes the star to expand. This is a very important point, and not an intiutive one, so you may have to do some more reading and thinking to understand it better.

Now, when the internal heat source dies, what happens? Well, the star starts to contract. This should be logical, if the star expands when the center gets hotter, when the center stops generating heat, the star should collapse.

Thus, when the star runs out of all its fuel sources, it starts to contract. If it's big enough, nothing can stop the process, and the star collapses into a black hole.

 

[RoboSapien]

What will happen to a star that is the size of most massive stars in the Universe and is made up completely out of URANIUM ?

What will happen to that star in the end ? or will it ever become a star in the first place even though humans do extract lot of energy out of the URANIUM ?

What makes a star into blackHole instead of further fusion of matter ?

 

[pervect]

What will happen to a star that is the size of most massive stars in the Universe and is made up completely out of URANIUM ?

What will happen to that star in the end ? or will it ever become a star in the first place even though humans do extract lot of energy out of the URANIUM ?

What makes a star into blackHole instead of further fusion of matter ?

I doubt that anyone has performed detailed calcuations on such an unlikely entity as a "star" made entirely out of uranium. I'd expect, though, that it would "burn" for a while (by fission, not fusion), eventually go out, and then collapse into a black hole if it was above the critical mass.

What determines when a star collapses into a black hole and when it does not is how large it's mass is.

The first phase of collapse, to electron degenerate matter, would still preserve the atomic structure of the matter that created it - in your thought experiment, uranium.

see for instance for more detail
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/whdwar.html

The next phase of collapse, to a neutron star, makes the atomic structure of the matter that formed the star utterly irrelevant. The star becomes in essence one giant nucleus. This happens if the size of the star exceeds Chandrasekhar's limit.

A neutron star also has a mass limit, but it doesn't have a name that I'm aware of. If this limit is exceeded, even the nuclear forces are not strong enough to keep the star from collapsing into a black hole. It doesn't matter what the atomic structure of the matter is (or was) to the collapse process - this information becomes irrelevant even before the final collapse to a black hole, when the "neutron star" stage is reached.

 

[RoboSapien]

...
The next phase of collapse, to a neutron star, makes the atomic structure of the matter that formed the star utterly irrelevant. The star becomes in essence one giant nucleus. This happens if the size of the star exceeds Chandrasekhar's limit.

A neutron star also has a mass limit, but it doesn't have a name that I'm aware of. If this limit is exceeded, even the nuclear forces are not strong enough to keep the star from collapsing into a black hole. It doesn't matter what the atomic structure of the matter is (or was) to the collapse process - this information becomes irrelevant even before the final collapse to a black hole, when the "neutron star" stage is reached.

So a neutron star can form but there is no fusion yet ?

And why is nuclear fusion possible only with elements lighter that iron ?

 

[selfAdjoint]

So a neutron star can form but there is no fusion yet ?

And why is nuclear fusion possible only with elements lighter that iron ?

No the neutron star forms after all the fusion has stopped, if the star was big enough.

As for the fusion stopping at iron, google on curve of binding energy. With lighter elements you get extra energy out of fusion, which helps to make more fusion.

 

[pervect]

A star is a big ball of gas. When you heat it up, it expands, just like any other ball of gss. For a normal HOT hydrogen stars, in fact, you can even use the ideal gas law, PV = nRT. (When the star gets too dense, the pressure is actually higher than given by this relationship).

Combine this with the normal fact that pressure increases with depth by the relation
delta-Pressure = density*g*delta-h, g being the local acceleration of gravity, and you have the equations you need to model stellar structure at a very basic level. Note that this formula is the same formula you use to calculate the pressure at the bottom of a water tank, except that the for water tanks the density of water and the gravitational acceleration g are both constant, where as neither of these are constant in stars.


For a non-relativistic model you'd use Newtonian gravity, for a fully relativistic star you need to use general relativity to determine the gravity.

http://www.astronomynotes.com/starsun/s7.htm

looks like a good reference if you want to read a little more.

 

[RoboSapien]

pervect

selfAdjoint

Thank U very much , I am satisfied except on the Uranium star issue.

 

[cherlin]

In 2002 the European Southern Observatory published the orbit of a start that was observed to pass within a few light-hours of SgrA*, which is several million solar masses. I keep the picture on my computer desktop. The mass can be determined from the orbit of the star using Kepler's laws. There is no way that millions of stars the size of the sun could be packed into a space the size of the solar system without collapsing into a black hole, so the inference is that SgrA* is a black hole formed billions of years ago.

Einstein didn't like quantum mechanics (which he helped found with his 1905 paper on the photoelectric effect), particularly the Uncertainty Principle and the probability wave equation, but QM "explains all of chemistry and most of physics" and is the basis for computers, lasers, photography, and a lot of other technology. He would have liked string theory better, and his lifelong search for the Unified Field Theory has been continued with the search for the Theory of Everything.

Einstein was smart, but he didn't know everything, as is always the case. Newton was big on alchemy, and Galileo refused to consider the possibility of the sun and moon raising tides in the ocean. "Occult forces", he called it.