Does gravitational energy travel like electrical energy?

[Orthoceras]

TL;DR Summary

Does gravitational energy travel like electrical energy?

Electrons flowing through a resistor are dissipating electrical energy. The electrical energy is transported from the battery to the electrons along the curved field lines of the Poynting vector. It seems like a meaningful idea that electrical energy necessarily travels from the source to the dissipation site.

My question is, does this idea somehow apply to gravitational energy as well? For example, consider a steady stream of sand falling through the air, from a funnel to the ground. Is the gravitational energy actually transported from the source (i.e., the funnel or the ground) to the dissipation site, where sand particles experience air resistance? If not, does gravitational energy not travel? Is gravitational energy more elusive than electrical energy?

 

[Ibix]

There are a lot of similarities between electromagnetism and gravity, but there are a lot of differences too. When thinking about flowing "charge" you have to remember that there are no opposite charges, so there's nothing quite like a current in a wire with a net zero charge. Also, like charges attract so the dynamics are rather different. Furthermore, localising energy in a gravitational field is notoriously difficult in all but the very simplest of circumstances, so it can prove very difficult to ask (rigorously) if energy has flowed anywhere.

So, as far as I understand it the "answer" to your query in general is that we don't really have a way to answer.

However, there are cases where you can argue that energy has transferred through the gravitational field. Gravitational waves are one such - Feynman pointed out that a pair of beads on a straight wire should move together and apart under the influence of a passing gravitational wave, and friction with the wire would generate heat, presumably sapping energy from the wave. And you can use the Penrose process to sap angular momentum from a black hole, again presumably passing energy through the field since there's nothing to touch.