Gravitational Collapse

[MigL]

Black holes and the ultimate fate of massive stars is predicted by GR,is backed up by indirect observation and is more-or-less generally accepted fact.

I have always wondered about other effects and their plausability, and maybe some of the members ( DrR where are you ? ) who are better versed in GR than I am can provide some guidance.

 

Consider an arrangement of massive stars all going supernova at the exact same time, and collapsing to black holes at the same time ( I know, not possible, but humour me ).

At the moment the Swartzchild radius is reached, a massive gravity wave leaves each collapsing star. Now imagine that the arrangement of the original stars is such that these resultant gravitational waves interfere constructively, leading to a massive gravitational energy density at a specific point. If this gravitatinal energy is dense enough, can it collapse to form a black hole even though no actual matter mass has collapsed ?

 

I know J.A. Wheeler did some work on stable energy orbits in the 50s and found that the energy density of these 'geons' was enough to keep the enrgy itself in a very unstable circular orbit ( donut shape ) and the slightest deviation led to dissipation or gravitational collapse. And it makes sense since energy and mass are equivalent. But this was trictly EM energy.

 

Has anyone investigated the gravitational collapse of gravitational energy of sufficient density ?

Edited August 24, 2011 by MigL

[csmyth3025]

...Has anyone investigated the gravitational collapse of gravitational energy of sufficient density ?

I can't answer your question, but I have one that's related: In the gravitational collapse of a star, does the intensifying gravity of the collapsing core contribute to the stress-energy-momentum tensor?

 

In the case of a stellar core collapse I'm thinking that the (negative) gravitational potential energy of the in-falling matter is being converted to (positive) gravitational binding energy.

 

This is a bit off-topic, so if it requires more than a yes-or-no answer I'll put it in a separate thread.

 

Chris

[IM Egdall]

I can't answer your question, but I have one that's related: In the gravitational collapse of a star, does the intensifying gravity of the collapsing core contribute to the stress-energy-momentum tensor?

 

In the case of a stellar core collapse I'm thinking that the (negative) gravitational potential energy of the in-falling matter is being converted to (positive) gravitational binding energy.

 

This is a bit off-topic, so if it requires more than a yes-or-no answer I'll put it in a separate thread.

 

Chris

 

Are you referring to the increase in pressure as the star collapses? Pressure I think is the flow of momentum and is a source of gravity in general relativity. So as the star compresses, the added pressure does contribute to the stress-energy-momentum tensor, increasing the collapse.

[Mystery111]

Black holes and the ultimate fate of massive stars is predicted by GR,is backed up by indirect observation and is more-or-less generally accepted fact.

I have always wondered about other effects and their plausability, and maybe some of the members ( DrR where are you ? ) who are better versed in GR than I am can provide some guidance.

 

Consider an arrangement of massive stars all going supernova at the exact same time, and collapsing to black holes at the same time ( I know, not possible, but humour me ).

At the moment the Swartzchild radius is reached, a massive gravity wave leaves each collapsing star. Now imagine that the arrangement of the original stars is such that these resultant gravitational waves interfere constructively, leading to a massive gravitational energy density at a specific point. If this gravitatinal energy is dense enough, can it collapse to form a black hole even though no actual matter mass has collapsed ?

 

I know J.A. Wheeler did some work on stable energy orbits in the 50s and found that the energy density of these 'geons' was enough to keep the enrgy itself in a very unstable circular orbit ( donut shape ) and the slightest deviation led to dissipation or gravitational collapse. And it makes sense since energy and mass are equivalent. But this was trictly EM energy.

 

Has anyone investigated the gravitational collapse of gravitational energy of sufficient density ?

 

Yes we have measured the gravitational collapse of a star mathematically. Is this what you mean? Some of your questions are incoherent though, like: ''If this gravitatinal energy is dense enough, can it collapse to form a black hole even though no actual matter mass has collapsed ?''

 

If you mean measured by observation, then no, we are yet to directly observed the collapse a superdense object, or an object with sufficient mass into that of a black hole.

[MigL]

No, i thought I was being rather clear.

 

Can you have a gravitational FIELD which has enough energy density to collapse and form an event horizon without any matter mass actually being involved in the collapse.

This would depend on the way gravitational energy ( potential ) is handled by GR, as opposed to mass/energy.

[Mystery111]

I don't know of any cases of a gravitational collapse without matter.

[questionposter]

What is the exact amount of force of gravity needed to shove an electron into the nucleus? Or what else happens to an atom just before an object becomes a black hole? What's the gravitational force needed to force neutrons together at such a high force they somehow break down and fuse? Or, since particle's can't escape, what happens to the component particles of things like protons and electrons just before they get forced together or when they actually do get forced together?

Edited August 30, 2011 by questionposter

[Mystery111]

An electron won't reach a nulceus because this is forbidden by the Uncertainty Principle. I would pressuppose it would take more energy in the visible universe to make an electron settle into the nuclei of atoms. Also stable orbits are obtained using a wave function of matter, so it's redundant to think that atoms can drastically deplete in energy.

Edited August 30, 2011 by Mystery111

[csmyth3025]

What is the exact amount of force of gravity needed to shove an electron into the nucleus? Or what else happens to an atom just before an object becomes a black hole? What's the gravitational force needed to force neutrons together at such a high force they somehow break down and fuse? Or, since particle's can't escape, what happens to the component particles of things like protons and electrons just before they get forced together or when they actually do get forced together?

Regarding electron degeneracy pressure (white dwarfs) and the force needed to "shove an electron into the nuleus":

 

...{an electron}Degenerate gas can be compressed to very high densities, typical values being in the range of 10,000 kilograms per cubic centimeter.There is an upper limit to the mass of an electron-degenerate object, the Chandrasekhar limit, beyond which electron degeneracy pressure cannot support the object against collapse. The limit is approximately 1.44 solar masses for objects with compositions similar to the sun. The mass cutoff changes with the chemical composition of the object, as this affects the ratio of mass to number of electrons present. Celestial objects below this limit are white dwarf stars, formed by the collapse of the cores of stars that run out of fuel. During collapse, an electron-degenerate gas forms in the core, providing sufficient degeneracy pressure as it is compressed to resist further collapse. Above this mass limit, a neutron star (supported by neutron degeneracy pressure) or a black hole may be formed instead...

 

 

 

-and-

 

 

Neutron degeneracy is analogous to electron degeneracy and is demonstrated in neutron stars, which are primarily supported by the pressure from a degenerate neutron gas.^[3] This happens when a stellar core above 1.44 solar masses, the Chandrasekhar limit, collapses and is not halted by the degenerate electrons. As the star collapses, the Fermi energy of the electrons increases to the point where it is energetically favorable for them to combine with protons to produce neutrons (via inverse beta decay, also termed "neutralization" and electron capture). The result of this collapse is an extremely compact star composed of nuclear matter, which is predominantly a degenerate neutron gas, sometimes called neutronium, with a small admixture of degenerate proton and electron gases.

(ref. http://en.wikipedia....generate_matter )

 

If you want more details than this, you'll probably have to find a physicist to explain it.

 

Chris

[MigL]

And further to Chris's reply, yes Electrons can settle into the nucleus.

 

The uncertainty principle doesn't say you cannot fix the location of an electron to an arbitrarily small space, rather location and momentum cannot be fixed to arbitrarily small values. In other words if you fix the location of an electron to the nucleus or smaller, its momentum ( energy ) can assume wild and large excursions. The upper limit for the momentum, and I believe the method Subrahim Chandrashekar ( spelling ?? ) used in his calculation on his way to London to see Eddington, is then the speed of light. That gives values for electron degeneracy pressure to counteract gravity.

 

Note that I'm not asking wether gravitational collapse of an extremely strong gravitational field is probable, it most likely isn't, notice the scenario needed to make 'favourable' conditions for it. I'm asking wether GR allows it or it is possible.

Edited August 30, 2011 by MigL