Gravity & Photons: Dynamics of a Hypothetical Closed Universe

[moving finger]

I am interested in looking at the dynamics of a hypothetical static (ie space not expanding or contracting) and closed "universe" filled only with radiation (only photons, no matter). (similar to Penrose's "Hawking's Box" - a closed universe in a box with perfectly reflecting walls so that no energy or fields escape the box).

Would such a universe exhibit gravitational clumping (ie would the photons attract each other gravitationally)? If yes, what are the equations governing the dynamics, and where can I get more information on this?

I would expect the gravitational clumping would depend on the photon energy density (eV/m3) and the mean photon frequency (energy per photon, eV). For sufficiently low energy density, or sufficiently high energy per photon, I would expect the "universe" to remain homogeneous and not exhibit gravitational clumping - is this correct? Is such a universe stable, or would it evolve over time to a more stable configuration?

If there is gravitational clumping, could Black Holes be formed, and if yes how would the mean Black Hole density be related to the background photon energy density and energy per photon at equilibrium?

Thanks for your help!

 

[Nereid]

Several days without an answer, yet >30 views; I'm moving this to SR&GR ... may get a quicker answer there ...

 

[1123581321]

it would not 'clump together', gravity with subatomic particles is not important and has no real effect.

Fibonacci

 

[pervect]

I am interested in looking at the dynamics of a hypothetical static (ie space not expanding or contracting) and closed "universe" filled only with radiation (only photons, no matter). (similar to Penrose's "Hawking's Box" - a closed universe in a box with perfectly reflecting walls so that no energy or fields escape the box).

Would such a universe exhibit gravitational clumping (ie would the photons attract each other gravitationally)? If yes, what are the equations governing the dynamics, and where can I get more information on this?

I think the answer is probably no. (Alert: I'm not positive, I haven't actually tried to work this out in detail). The pressure on a small "box" of photons is going to be the maximum possible pressure that can be generated with that amount of energy.

On a local scale, I don't see how clumping would be possible, I think the high pressure and the hydrodynamic equations will prevent it.

On a cosmological scale, the universe as a whole could still collapse - but I don't think it will tend to form any "clumps" while doing so.

I wonder if anyone has looked at this seriously - if this is really true, it ought to make the collapse of a radiation-dominated black hole especially easy to model and compute.

 

[moving finger]

it would not 'clump together', gravity with subatomic particles is not important and has no real effect.

Fibonacci

Surely not?
Surely it depends on the density and volume of matter/radiation?
Even photons have an effective mass by e=mc^2 and will exert gravitational attraction on each other. I agree the effect will be small between any two photons, but if you have enough of them in a small enough volume then surely gravitational effects will dominate?

MF

 

[1123581321]

Surely not?
Surely it depends on the density and volume of matter/radiation?
Even photons have an effective mass by e=mc^2 and will exert gravitational attraction on each other. I agree the effect will be small between any two photons, but if you have enough of them in a small enough volume then surely gravitational effects will dominate?

MF

you do have a point, but i am no expert on this sort of stuff, so i just pretend to be educated on the matter. besides, it is really not my fault, i havn't had any real physics in HS yet, that will be my senior year. (don't laugh at my age)

Fibonacci

 

[selfAdjoint]

Photons
1. Are bosons and can clump quantally.
2. Gravitate, so they can be made to clump.

There is an argument that any gravitating "dust", at least in the deSitter form of general relativity, will clump. Photons are such a dust.

I say they will not only clump but will eventually form a BEC.

 

[pervect]

Photons
1. Are bosons and can clump quantally.
2. Gravitate, so they can be made to clump.

There is an argument that any gravitating "dust", at least in the deSitter form of general relativity, will clump. Photons are such a dust.

I say they will not only clump but will eventually form a BEC.

Things have been rather slow recently - maybe we could have an argument?

Let's start with some definitions. I'd call a system gravitationally bound if it's components didn't have enough energy to escape.

This is going to be a key point in the argument.

For cold matter, this is fairly easy to accomplish. But for photons, the smallest bound system via this defintion is a black hole, which occurs when the escape velocity of the bound system is the speed of light.

If we have a big "universe", consisting of matter, I can envsion clouds of it forming locally gravitationally bound systems (i.e. stars, like we have in our universe).

But I can't imagine that working for photons - if the universe is reasonably isotropic, and one section of the universe contains a high enough density of photons to form a black hole, a larger section of the universe would contain enough energy to form a larger black hole. So I think that a universe of photons should collapse to one black hole, if it's going to collapse at all. If it doesn't have a great enough density to form even one black hole, no "gravitationally bound systems" can form at all.

 

[selfAdjoint]

Things have been rather slow recently - maybe we could have an argument?

Let's start with some definitions. I'd call a system gravitationally bound if it's components didn't have enough energy to escape.

This is going to be a key point in the argument.

For cold matter, this is fairly easy to accomplish. But for photons, the smallest bound system via this defintion is a black hole, which occurs when the escape velocity of the bound system is the speed of light.

If we have a big "universe", consisting of matter, I can envsion clouds of it forming locally gravitationally bound systems (i.e. stars, like we have in our universe).

But I can't imagine that working for photons - if the universe is reasonably isotropic, and one section of the universe contains a high enough density of photons to form a black hole, a larger section of the universe would contain enough energy to form a larger black hole. So I think that a universe of photons should collapse to one black hole, if it's going to collapse at all. If it doesn't have a great enough density to form even one black hole, no "gravitationally bound systems" can form at all.

I was thinking of particles in a box. By lining the box with "perfect mirrors" (this is a thought experiment after all!), you can keep the photons inside.

 

[moving finger]

I was thinking of particles in a box. By lining the box with "perfect mirrors" (this is a thought experiment after all!), you can keep the photons inside.

Yes, this is what I was thinking as well. A finite space but with perfectly reflecting "walls" so that no energy is lost. Then you have a mean energy density due to photons; if that mean energy density is above a certain limit then surely the photons will gravitate, possibly forming one or more black holes?

This is the photon-equivalent of Hawking's Box (read Penrose for more info, or see the paper at http://arxiv.org/abs/hep-th/0410270 section 4).

What is the critical photon energy density, above which gravitation will occur?

Is it essential that Black Holes will form?

Will there be only one Black Hole, or could there be several (if clumping occurs then this would tend to result in regions which have more or less than the critical photon energy density)?

 

[joshuaw]

But wouldn't some of these photons start forming particle anti particle pairs, which would in turn eventually lead to EM considerations?

Josh

 

[selfAdjoint]

What is the critical photon energy density, above which gravitation will occur?

Why would there be any critical energy? Any photon has SOME energy and would contribute to the stress-energy-momentum tensor in general relativity.

 

[pervect]

A couple of comments - in a box of photons, I would expect that gravitational self-interaction would make the measured frequency of the photons near the center of the box ever-so-slightly higher than at the edges. This would correspond to an uneven distribution of energy, which could be regarded as a "clumping" of energy in the center. I don't think the phenomenon would be experimentally measurable with existing technology, it's more of a thought experiment.

But unless the photons are dense enough to form a black hole, one won't have a "bound system". I think that this also mplies that if any transient clumping of photons higher than equilibirum occurs, he clumping will not progress, unless the "black hole" threshold is exceeded. So I don't think the clumps can be stable, they will tend to dissipate and will exist only if forced by the boundary conditions (the walls of the box).

I was originally going to ask for some help on a totally unrelated aspect of the box-of-photons problems that was bothering me, but I think I've got some ideas on how to proceed.

 

[moving finger]

Why would there be any critical energy? Any photon has SOME energy and would contribute to the stress-energy-momentum tensor in general relativity.

I said critical energy-density, not critical energy.

Energy density translates to graitational attraction.

Why should there be a critical energy density? Because if pervect is correct (see his last post in this thread), then unless the energy density is high enough to form a black hole, the system will not be gravitationally bound.

MF