Gravitomagnetic Waves: Properties & Sources

[espen180]

An occilating charge creates an electromagnetic wave of speed $$\frac{1}{\sqrt{\epsilon_0\mu_0}}$$.

Since Maxwell's equations hold for gravitomagnetism, an occilating mass should create a gravitomagnetic wave with the speed $$\sqrt{\frac{4\pi G}{\mu_g}}$$. (mu_g is a "gravitomagnetic vacuum permeability")

If this is so, what are the properties of gravitomagnetic waves?

 

[Jonathan Scott]

An occilating charge creates an electromagnetic wave of speed $$\frac{1}{\sqrt{\epsilon_0\mu_0}}$$.

Since Maxwell's equations hold for gravitomagnetism, an occilating mass should create a gravitomagnetic wave with the speed $$\sqrt{\frac{4\pi G}{\mu_g}}$$. (mu_g is a "gravitomagnetic vacuum permeability")

If this is so, what are the properties of gravitomagnetic waves?

Changes in the gravitational field propagate at the speed of light, the same as for electromagnetism. These include both linear components (equivalent to electric field) and rotational components (equivalent to magnetic field).

Creating a detectable gravitational wave is difficult because of conservation of energy and momentum; you can only make a mass wobble significantly by using another mass and a supply of energy, but as that must be around the same location, it means that the overall energy is unchanging and the best you can do is change its orientation or shape, causing tidal effects.

 

[Vanadium 50]

Since Maxwell's equations hold for gravitomagnetism,

I've not heard of such a thing, but if this is the case, it can't be correct. Maxwell's equations support dipole radiation. Gravity has no dipole radiation; the lowest multipole is quadrupole.

 

[espen180]

I was really talking about gravitomagnetic theory. The equations I had in mind are these: http://en.wikipedia.org/wiki/Gravitomagnetism#Equations

 

[Jonathan Scott]

I was really talking about gravitomagnetic theory. The equations I had in mind are these: http://en.wikipedia.org/wiki/Gravitomagnetism#Equations

Yes, but as I explained (obviously not clearly enough) you can't create the same sort of first-order waves as in electromagnetism, because there isn't a way of moving masses around without using other masses and energy. That is, there is simply no way to "wobble" the center of mass of a complete system.

You can spread mass out in different ways; for example a pair of masses aligned towards the observer has a slightly different gravitational field from a pair of masses with the same center of mass aligned tangentially to the direction to the observer, so by rapidly rotating one mass around another you can create a very slight change. However, the whole gravitomagnetism scheme is a linear approximation and I don't think that this type of tidal change (quadrupole radiation) can be described within it.

 

[espen180]

Okay, now I understand that gravitomagnetic waves are a more complicated story than electromagnetic ones. I have some questions though.

One thing I don't right understand is why the center of mass of a system can't be wobbled. Are you referring to the conservation of momentum? In that case, a pendulum fastened to the ground would not be a complete system by itself, because I have to take it's effect on the Earth into account as well?

Also, I find it difficult to understand why utilizing mass and energy in order to occilate another mass is a problem when trying to make gravitomagnetic waves. Is it related to the above paragraph?

 

[Jonathan Scott]

Okay, now I understand that gravitomagnetic waves are a more complicated story than electromagnetic ones. I have some questions though.

One thing I don't right understand is why the center of mass of a system can't be wobbled. Are you referring to the conservation of momentum? In that case, a pendulum fastened to the ground would not be a complete system by itself, because I have to take it's effect on the Earth into account as well?

Also, I find it difficult to understand why utilizing mass and energy in order to occilate another mass is a problem when trying to make gravitomagnetic waves. Is it related to the above paragraph?

Yes, a pendulum is not a complete system. Neither is a rocket, if you fail to include its exhaust gases or other propellant.

From a sufficient distance, the gravitational effect of any system is equivalent to the effect of its total energy located at its center of mass. Since conservation laws mean that there is no way to wobble that center of mass, there is no way to create waves equivalent to those produced by wobbling a charge.

Even if you push and pull something using a long thin rod, you are still transferring energy, and the complete system including that energy and whatever the pushing or pulling is working against still has the property of having constant total energy and momentum, and a center of mass which has a fixed velocity.