Yor_on, I think you're making this question way too complicated for an easy answer by jumping immediately to gravitational radiation.

Let's go back to the very basic, first question you asked, which is whether gravity is equivalent to energy. Like I said, it isn't equivalent. There are two equations that tell you what gravity does:

1) Einstein's field equations, which you posted above, and which tell you how space-time bends due to a

**stress-energy** tensor. The stress-energy tensor contains information about the amount and flow of momentum and energy of masses and electromagnetic fields in space and time.

2) Geodesic motion, which says that when you put a mass in space-time, it will follow geodesics unless it's accelerated somehow.

When you combine these, you have a description of how space bends and how objects move within that bending. This describes gravity.

The only equation which could be said to be due to energy is the first one--the bending of space-time. If you really wanted to confuse people, you could say that the bending of space time is "equivalent" to the stress-energy tensor, since Einstein's field equations have the bending terms on one side and the stress-energy tensor on the other. I think it's much less confusing if you think about the curvature as being due to the presence of mass. But even in that case, all you've done is to say that the presence of a mass causes a gravitational field due to the mass's inherent energy (E=mc

^{2}), or more properly, the mass's stress-energy tensor.

Let's see Einstein's field equations again:

G_{mu},_{nu} = 8pi T_{mu},_{nu}

The left-hand side describes the bending of space-time and the right-hand side is the stress-energy tensor, which includes contributions from things in space-time, but not space-time itself: the information about space-time and it's bending is entirely contained in the left-hand side of the equation.

Now, you can chop up the left-hand side into terms so that one of them looks like the "energy" of the gravitational field, and move it over to the right hand side, so that you now have a "stress-energy" term for gravity, then it appears that curvature depends on the energy of the gravitational field. But the problem is that the right-hand side is no longer reference frame invariant, meaning that this physical law varies depending on where you are in space. So you can't really point to a spot in space-time and say "I know the energy there."

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As I understand it, though, there are some cases where you can talk about the energy due to the bending of space-time. One of those is when you're far away from a gravitating object, so space-time near you is nearly flat. All observers far away will agree with you on your definition of energy. I believe this is how they get to gravitational radiation carrying away energy. Gravitational waves escape from the region around the gravitating objects and propagate far away from them. In this far-away region, you can define an energy being carried by these waves, and then clearly, the energy of the total field near the objects will decrease as a result of gravitational radiation.

What happens as a result of this energy loss? Newton's laws should still approximately hold, and in that case, energy loss leads to decaying orbits. Therefore in the gravitational wave case, the orbits should decay, or in other words, they begin to orbit closer to each other, which leads to a configuration of space-time that has less total energy as you measure it from far away...

And all that comes with my usual disclaimer about not being an expert, of course.