Energy analogs in expanding/collapsing dust universes

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Spinnor
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I think in a piece by John Baez we learn that the physics of an expanding and collapsing dust filled universe is the same as the physics of a bouncing ball,
Radius, R, verses time and height, h, verses time?

If so are there counterparts to the kinetic and potential energy of a bouncing ball and an expanding and colapsing dust filled universe? It seems that when R and h are maximum we have max potential energy and when R and h are near zero we have max kinetic energy, if General Relativity has "things" like potential and kinetic energy?

If you and I were nearby dust particles, in an expanding and collapsing universe, in the expansion stage say, we could estimate our potential and kinetic energies of each other by observation? I can "measure" your distance and velocity and thus estimate kinetic and potential energy? If

When a gravitational wave goes by does space-time kind of "vibrate"? If so can we identify parts of the energy of a gravitational wave as being part "kinetic" and part "potential"?

Could an oscillating dust filled universe be considered a "standing wave" because the potential and kinetic energy are 90 degrees out of phase?

Thanks for any help!
 
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When a gravitational wave goes by does space-time kind of "vibrate"? If so can we identify parts of the energy of a gravitational wave as being part "kinetic" and part "potential"?
Gravitational and electromagnetic waves are closely similar. Can you do this for an electromagnetic wave?

Think - the electromagnetic energy density is (E2 + B2)/2. But in an electromagnetic wave, E and B are in phase. They reach maximum at the same time, and fall to zero at the same time. So the analogy with a mechanical wave, where energy goes back and forth between a "kinetic" part and a "potential" part simply does not hold. Like for gravitational waves.
 
Bill_K said:
Gravitational and electromagnetic waves are closely similar. Can you do this for an electromagnetic wave?

Think - the electromagnetic energy density is (E2 + B2)/2. But in an electromagnetic wave, E and B are in phase. They reach maximum at the same time, and fall to zero at the same time. So the analogy with a mechanical wave, where energy goes back and forth between a "kinetic" part and a "potential" part simply does not hold. Like for gravitational waves.

Unless we have a standing E and M wave?
 
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Bill_K said:
How is that different? E and B are still in phase.

In a standing wave its all E and then all B? I would normally defer to your expertise but I think you are wrong.