infinite gravity

[dstebbins]

When a star experiences gravitational collapse, it goes down to a point of zero size, and its gravity becomes infinite. I can see this being explained in two ways:

 

1. In GR, density is factored into the equation for gravity, as opposed to the Newtonian theory of gravity, or

 

2. The laws of Thermodynamics state that if you compress an object while keeping its mass the same, it gets hotter, so if you compress it to zero size (aka infinite density), it becomes infinitely hot, and according to e=mc^2, infinite energy = infinite mass = infinite gravity.

 

Which is it?

[Riogho]

It doesn't go down to zero size. It's gravity isn't infinite.

[dstebbins]

I'd like to see some documentation on this, because what I read in Stephen Hawking's book A Brief History of Time says the exact opposite.

[ydoaPs]

I'd like to see some documentation on this, because what I read in Stephen Hawking's book A Brief History of Time says the exact opposite.

 

The magnitude of force of gravity between two objects is given by [math]|\vec{F}|=G\frac{{m_1}{m_2}}{r^2}[/math] where G is the gravitational constant, m₁ and m₂ are the masses of two objects, and r is the distance between them. The magnitude of the gravitational field at a distance is given by [math]|\vec{G}|=G\frac{M}{r^2}[/math] where G is once again the gravitational constant, M is the mass of the object whose gravitational field is being measured, and r is the distance from the object. Note that these equations treat the mass as though it were all concentrated in a dimensionless point(i.e. it has infinite density)

[Janus]

As a star collapses to zero size, its surface gravity approaches infinity. This is due to the fact that the Newtonian gravitation equation is:

 

[math]A_g = \frac{M}{r^2}[/math]

 

Where Ag is the acceleration due to gravity.

 

As the star collapses r approaches 0 and thus Ag approaches infinity.

 

However, the total energy of the gravitational field, nor the acceleration due to gravity at a fixed distance does not change as the star collaspes. There is no difference in the force of gravity felt by an object a given distance from the star from before the collapse and after the collapse.

 

Thus there is no need to involve density in calculating the gravity.

 

As far as the thermodynamics go, In the case of the collapsing star, the increase in temperature comes from the the gravitational potential of the stars mass as it collapses. As the material of the star falls inward, it gives up potential energy for kinetic energy and the star gets hotter. But, the total energy of the star does not increase, there has just been a transfer from one kind of energy to another. Since the total energy of the Star was not infinite before the collapse, it will not be so after the collapse.

[Martin]

It doesn't go down to zero size. It's gravity isn't infinite.

I'd like to see some documentation on this

 

We don't yet have tested theories of quantum gravity, instead we have some more or less successful but still unproven CONJECTURES. So you presumably want documentation on the conjectures, and how the work is going at present.

 

For some 50 years (since Dirac at mid-century) the theorists involved with it have assumed that collapse does NOT proceed to zero size and that gravity does NOT become infinite. That happens in the context of General Relativity, a manmade theory, but there is no indication it happens in nature. What theorists have ordinarily supposed is that General Relativity WRONG or of limited applicability because it breaks down at certain failure points called singularities and predicts infinities (infinite curvature, density, temperature etc.)

 

For 50 plus years the expectation has been (by all kinds of theorists who thought about it, not just this school or that) that eventually a QUANTIZED General Relativity would cure the failures of the classical theory, and get rid of the singularities.

 

This field of research (usually called QG, understood to mean quantum General Rel, or quantum gravity) has recently started to move ahead very rapidly. I would advise not reading anything from before 2005.

 

Anything by Hawking will give you a misleading out-of-date idea.

 

The next big QG conference on this will be in England starting in late June 2008.

http://www.maths.nottingham.ac.uk/conferences/qgsquared-2008/

 

I don't know of any popularization writing about the current work. If you want DOCUMENTATION, as you say, then you should be prepared to skim technical papers. Journal articles usually have some non-technical discussion in the Introduction section at the beginning and in the Conclusions section at the end. So you can get some stuff out without delving into detail. I can give you links to several recent papers.

 

Here's one that appeared in October, for example.

 

http://arxiv.org/abs/0710.3565

On the robustness of key features of loop quantum cosmology

Abhay Ashtekar, Alejandro Corichi, Parampreet Singh

(Submitted on 18 Oct 2007)

 

"A small simplification based on well motivated approximations is shown to make loop quantum cosmology of the k=0 FRW model (with a massless scalar field) exactly soluble. Analytical methods are then used i) to show that the quantum bounce is generic; ii) to establish that the matter density has an absolute upper bound which, furthermore, equals the critical density that first emerged in numerical simulations and effective equations; iii) to bring out the precise sense in which the Wheeler DeWitt theory approximates loop quantum cosmology and the sense in which this approximation fails; and iv) to show that discreteness underlying LQC is fundamental. Finally, the model is compared to analogous discussions in the literature and it is pointed out that some of their expectations do not survive a more careful examination. An effort has been made to make the underlying structure transparent also to those who are not familiar with details of loop quantum gravity."

 

The gist is that whether they work numerically ( with computer models) or analytically ( by solving systems of equations) they always find that the density maxes out. Quantum gravity turns REPELLENT because of quantum corrections that dominate at very high density. So the collapse fails to achieve infinite smallness or infinite density. Density tends to max out before reaching a high value called "planck density"----some 10⁹³ times the density of water.

 

this is using one particular style of quantum gravity, but my guess is that as other QG approaches arrive at the same point of analyzing extreme gravitational collapse they also will find that there are quantum corrections which cause the infinities to be avoided.