How do gravitational waves transfer angular momentum in general relativity?

[kmarinas86]

PART 1

I know that beams of light can push objects. Sunlight affects the spin of asteriods.

Therefore light can transfer angular momentum from one object to another on contact.

But I could not find the definition of such angular momentum! Where does it come from?

I did a little research, but all I could find is angular momentum and orbital angular momentum, but they are nothing like what I am thinking of.

PART 2

If light does not have mass, then it cannot contribute to the center of mass. People say the center of mass is the center of gravity. If photons do not change the center of gravity, then they cannot apply torque to a celestial object at a distance, right?

People say there are no "forces" in GR, which implies that there is no such thing as torque in GR, since that requires a force over an angle. If there is no such thing as torque in GR, then nothing in GR describes a transfer of angular momentum, which is by definition a torque. Then, it would imply that GR cannot predict local changes in angular momentum! If that's the case, if a photon were emitted and absorbed in a direction offset from the center of a mass, it would produce a torque, but it would have nothing to do with GR. If GR described gravitational waves resulting in an angular acceleration of some particles, then it must have something to do with forces. In a space with curvature, force and angular acceleration are inseperable. You cannot say that GR does not predict forces if you say that it explains the rotational acceleration of massive objects!

Is my judgement in PART 2 correct?

 

[mgb_phys]

PART 1
I know that beams of light can push objects. Sunlight affects the spin of asteriods.

I don't think photon pressure does much to affect the spin of asteroids. It is more likely that it heats the surface and boils off volatiles creating thrust. This is actually more true of comets.
On a larger scale it is possible to use the photon pressure to create a solar sail http://en.wikipedia.org/wiki/Solar_sail

Therefore light can transfer angular momentum from one object to another on contact.

Light can transfer momentum, and if it hits a rotating object off-centre it will impart angular momentum.
Photons have a very small momentum given by P = h * frequency.
There is a device (whose name I have forgotten) with a black painted freely moving wheel in vacuum, it rotates from the photon pressure on the wheel panels

Sorry, I can't make any sense of part 2

 

[JoAuSc]

I can't answer part 2, but here's a stab at part 1:

Don't forget that an object traveling in a straight line can have angular momentum too. You can't talk absolutely about "angular momentum", just "angular momentum about this particular point".

Let's pick the sun as the origin of our coordinate system. To keep things simple, let's assume an asteroid is falling into the sun, but it's far enough away so that it'd take a while. The sun shines photons of light outwards; relative to the sun, these photons have no angular momentum (classically speaking) because they're going straight outwards. When they hit the asteroid, the photons will bounce in various directions that aren't parallel to the sun, so they will gain angular momentum relative to the sun. The asteroid will gain angular momentum too, both about its axis, and about the sun, and when you sum up the angular momenta of the photons and the asteroid, you should get zero.

So to answer your question, the net angular momentum doesn't change, so it doesn't come from anywhere. The asteroid's angular momentum changes, but that's offset by the gain in angular momenta by the photons as they bounce off into a direction that's no longer parallel to the sun.

 

[AlephZero]

There is a device (whose name I have forgotten) with a black painted freely moving wheel in vacuum, it rotates from the photon pressure on the wheel panels

The Crookes Radiometer. Crookes and Maxwell gave two different explanations of why it works, both of which were wrong.

Reynolds finally sorted it - and the cause isn't photon pressure at all.

http://math.ucr.edu/home/baez/physics/General/LightMill/light-mill.html

 

[mgb_phys]

TCrookes and Maxwell gave two different explanations of why it works, both of which were wrong.
Reynolds finally sorted it - and the cause isn't photon pressure at all.

You're right I rembered that Crooke got it wrong but I thought he only got the direction wrong because the photons are 'reflected' with a longer wavelength and lower momentum.
I hadn't realized it was a purely aerodynamic effect.

 

[Idjot]

PART 1

I know that beams of light can push objects. Sunlight affects the spin of asteriods.

Therefore light can transfer angular momentum from one object to another on contact.

The Yarkovsky effect explains the "sunlight-driven" movement of asteroids. But there is a part of the Yarkovsky effect you must consider. It's not the sunlight moving the asteroids directly. The sunlight heats them up and then the asteroids themselves emit infared radiation which moves them (ever so slowly - around 1000 miles in a billion years).

PART 2 is a notoriously tough one but not impossible so don't bail on GR :) - here's a link:

http://www.ligo.caltech.edu/LIGO_web/9902news/9902liv.html#Article_2

Here's a taste:

1.

"Specifically, we look at "null infinity"; the place and time far from all mass where gravity waves eventually reach. By looking here, one can obtain a definition that allows for the exchange of angular momentum through gravity wave emission."

2.

...by integrating over a sphere encompassing all the mass; this enables us to pick up the effects of the gravitational field because the integration samples globally rather than locally. The definition, thereby, becomes a non-local definition.