Self-Gravity of gravitational waves

[Jonny_trigonometry]

Gravitational waves theoretically effect themselves due to "self-gravity"
http://arxiv.org/abs/0704.1149

I thought this was interesting. From a layman's perspective, a wave is a bundle of energy distributed through the medium it's traveling through. In the case of gravity waves (which themselves are space-time distortions), their presence within space-time affects the curvature of space-time due to their energy. So gravity waves are unique, since their presence effects their own boundary conditions. Now consider a spherical distortion with such great energy-density that it bounds itself as a mini-black hole and forms a stable standing wave. Is this possible?

I'd imagine the math would be horribly complex, as the boundary conditions of the standing wave are dynamic and coordinated with the standing wave's structure, but maybe something special can be found, such as a discrete spectrum of frequencies and energies of stable solutions.

 

[Bill_K]

Gravitational waves theoretically effect themselves due to "self-gravity"
http://arxiv.org/abs/0704.1149

Notice this is a fairly subtle effect - plane gravitational waves do not self-attract. What he's talking about specifically is a spherical wave pulse climbing out of a Schwarzschild field. Since the pulse carries away some of the energy, the trailing edge of the pulse travels in a Schwarzschild field with slightly less mass as compared to the leading edge.

 

[PeterDonis]

In the case of gravity waves (which themselves are space-time distortions), their presence within space-time affects the curvature of space-time due to their energy. So gravity waves are unique, since their presence effects their own boundary conditions.

All types of waves carry energy, not just gravitational waves, so all types of waves affect the curvature of spacetime. The only way gravitational waves are "unique" is that they are waves *of* spacetime curvature; there is zero stress-energy tensor associated with gravitational waves, whereas any other kind of wave (e.g., an electromagnetic wave) will have a nonzero SET associated with it.

Now consider a spherical distortion with such great energy-density that it bounds itself as a mini-black hole and forms a stable standing wave. Is this possible?

Sort of. John Wheeler speculated about the possibility of a "geon", which is something like what you describe (at least, the gravitational version is):

http://en.wikipedia.org/wiki/Geon_(physics )

A geon wouldn't necessarily have to be a black hole (i.e., it wouldn't necessarily have to have an event horizon). Also, as you can see from the Wiki page, it is not known whether there really is an exact solution to the Einstein Field Equation of this nature; all the results so far are only approximate.

 

[Jonny_trigonometry]

Thats very interesting. The "geon" is pretty much what I was asking for I think. And now please pardon my following speculations, but let's entertain the idea for a moment, as Wheeler himself did:

"Wheeler speculated that there might be a relationship between microscopic geons and elementary particles"

I wonder if, first of all, there are stable configurations.

Secondly, it would be exciting to find if there is a discrete set of them, a quantized set. And that quantum numbers fall out due to some periodic relations that can be made, such as how Bohr first approached the hydrogen atom--to make the wavefunction periodic in the circumference of the electron's orbit. Perhaps one critereon of stability is the difference in energy-density between the inside and the outside of the geon (maybe higher energy particles are stable only within space-time that is of higher energy-density), this could explain why there seems to be a finite discrete set of stable elementary particles.

Thirdly, I wonder if there would be different types of sets depending on vibrational "modes". Whether they are spherical oscillations of space-time, or torsional oscillations, or if there can be a mainly time or mainly space component of oscillation. And would these different types of stable vibrational configurations exhibit different qualities that elementary particles exhibit?

The idea is fascinating. I've always wondered if there is a way to describe the particles as different configurations of space-time, but I've always thought of it in terms of static "knots". If they are dynamic, steady-state, self-contained oscillations of space-time, then that lends itself well with wave-particle duality of Quantum Mechanics.

By the way, I recognize that you may have already rightly concluded that I'm merely an engineer with no advanced degrees, and unaware of how stupid I may sound. One humble request... Go easy on me...

 

[PeterDonis]

All these are interesting speculations and many physicists have indeed speculated along these lines. Another one that I've always found interesting is the idea that there is a link between black holes and elementary particles: basically, since the minimum mass a BH can have is the Planck mass, perhaps BHs and elementary particles are analogous to bound and free states of something like an electron. Standard QM says that for a quantum particle, the spectrum of bound states is discrete, like the spectrum of elementary particles (only certain specific masses appear, and all of them are well below the Planck mass), while the spectrum of free states is continuous, like the "spectrum" of possible black holes (any mass above the Planck mass). The Planck mass would then be the "threshold" at which an elementary object is no longer bound, but free.

All we can say at this point is that all these are interesting speculations; AFAIK nobody has been able to work them into any kind of predictive theory. Some of the ideas have probably helped to contribute to string theory, loop quantum gravity, etc.

 

[Jonny_trigonometry]

Another one that I've always found interesting is the idea that there is a link between black holes and elementary particles: basically, since the minimum mass a BH can have is the Planck mass, perhaps BHs and elementary particles are analogous to bound and free states of something like an electron. Standard QM says that for a quantum particle, the spectrum of bound states is discrete, like the spectrum of elementary particles (only certain specific masses appear, and all of them are well below the Planck mass), while the spectrum of free states is continuous, like the "spectrum" of possible black holes (any mass above the Planck mass). The Planck mass would then be the "threshold" at which an elementary object is no longer bound, but free.

hmm... interesting. I'm more of the school of thought that mass is not an intrinsic characteristic of elementary particles, but just an emergent effect of space-time as it interacts with itself. For example, we can derive the property of mass entirely by allowing certain properties of space-time. Viewing space-time from the perspective of continuum mechanics, one property of space-time is that it has zero first order viscosity (Netwon's 3rd law) -- it doesn't resist a constant change in position over time. Another property of space-time is that it has a second order viscosity (Newton's 2nd law) -- it resists changes in velocity, and it's constant of proportionality has become known as mass, but we've been ascribing that characteristic to the thing in motion, not the thing that the thing is moving through. Though in this view, the thing in motion is made of the same stuff as the thing its moving through, but it's just in some particular stable configuration.

 

[Jonny_trigonometry]

The Planck mass would then be the "threshold" at which an elementary object is no longer bound, but free.
.

this reminds me of quantum confinement a little bit. That in a crystal, if an electron is freed from its binding atom, it orbits the newly created hole at a certain radius. If you make the size of the crystal smaller than the orbital radius, the density of excited states becomes quantized. You can "tune" the size of the band gap by controlling crystal growth.