Can gravitational waves do work?

Question

I was reading about how a large amount of mass is lost as gravitational waves, X-ray radiation, and gamma radiation during a kilonova. I also read about the sticky bead analogy to better understand how energy is carried by gravitational waves. But then can this energy be transferred over to matter? The friction in the sticky bead analogy isn't really an electromagnetic wave, right, so it can't transfer anything to matter I guess?

Answer 1

For up to a long time this was a topic of controversy, involving formal mathematical arguments. It was settled by a simple physical argument credited to Feynman:

Later in the Chapel Hill conference, Richard Feynman used Pirani's description to point out that a passing gravitational wave should in principle cause a bead on a stick (oriented transversely to the direction of propagation of the wave) to slide back and forth, thus heating the bead and the stick by friction. This heating, said Feynman, showed that the wave did indeed impart energy to the bead and stick system, so it must indeed transport energy, contrary to the view expressed in 1955 by Rosen.

Answer 2

I will proceed in two stages.

• I will first establish that tidal effect can do work.
• Then I will offer the consideration that a passing gravitational wave has a tidal effect.

Let a moon be orbiting a planet in an eccentric orbit.

For comparison I will first discuss the case of circular orbit, with the moon in tidal lock. In that motion there is tidal effect, but it has no consequences. The tidal effect causes an elongation of the moon, along the radial direction. With the moon in tidal lock the orientation of the tidal effect with respect to the interior of the moon remains constant, as a consequence there is no opportunity to do work.

When the moon is in an eccentric orbit the tidal effect has a significance that it doesn't have in circular orbit case. Closer to the planet the gradient in graviational potential energy is steeper. So: for a moon in eccentric orbit the magnitude of the tidal effect is not constant. During the journey towards closest approach the magnitude of the tidal effect increases. During the climb to furthest distance the magnitude of the tidal effect decreases.

The effect of the non-constant magnitude of tidal effect is that the moon is being "kneaded". The (periodic) change in magnitude of tidal effect has as result a (periodic) change in magnitude of physical elongation.

The connection with work done is as follows:
A celestial body tends to contract itself into spherical shape; the spherical state is a state of lowest possible potential energy. For a celestial body to shift to be in an elongated state is to be in a state of higher potential energy than the spherical lowest-possible-state.

The process of relaxing back to a lower elongation state is a process of releasing potential energy. That is the connection with work done.

Condition for dissipation of energy

If the moon would be in a state of superfluidity then the "kneading" due to the change in magnitude of tidal effect would not lead to dissipation of energy. (Superfluidity in the sense of the state of superfluidity that Helium goes to when cooled below 2.17 Kelvin.)

But of course the moon in this thought demonstration is not in a state of superfluidity. Just as dough increases in temperature as it is being kneaded the process of the moon being "kneaded" generates heat.

Gravitational wave and tidal effect

A gravitational wave has a tidal effect. In the absence of a gravitatioanal wave spacetime is uniform. A gravitational wave is a quadrupole wave with a corresponding tidal effect. Since the gravitational wve is propagating: the passage of a graviational wave means a passing oscillation in tidal effect.

Answer 3

Yes, gravitational waves can do work. When they pass through an object, they cause stretching and contraction of that object which requires energy.

Answer 4

Very simple answer: Since they carry energy away when they are created, they can also deposit energy in the same way.

It's the principle of reversibility that applies throughout physics (with important exceptions). If you have a process, that same process can run in reverse. Because the equations that govern these processes are symmetric about time. Since gravitational waves are created by accelerated masses, they are also able to accelerate masses. So, if you have two bodies that rotate around each other at the same frequency that some merging black holes did, you will find that those bodies may get a tiny kick from the passing gravitational wave. Whether that kick is positive or negative will depend on the exact phase angle between the rotating bodies and the wave.