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ROGER PENROSE IN THE ROAD TO REALITY chap 19 WROTE:

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"Although there is no room for such a thing in the energy–

momentum tensor T, it is clear that there are situations where a ‘disembodied’

gravitational energy is actually playing a physical role.

Imagine two massive bodies (planets, say). If they are close together (and we can

suppose that they are instantaneously at rest relative to each other), then

there will be a (negative)

gravitational potential energy contribution whichmakes the total energy, and therefore the total mass, smaller than it would. Ignoring much tinier energy effects,be if they are far apartsuch as distortions of each body’s shape due to the gravitational tidal field

of the other, we see that the total contributions from the actual energy–

momentum tensor T will be the same whether the two bodies are close

together or far apart. Yet, the total mass/energy will differ in the two cases,

and this difference would be attributed to the energy in the gravitational

field itself (in fact a negative contribution, that is more sizeable when the

bodies are close than when they are far apart)."

--------------

The same problem was also rised by

Thirring, Kalman and Feynman in the FGT theory, they inserted the gravitational energy in the tensor equations...It is a problem of paramount importance which prevents theGeneral relativity theory from describing any motion in which the hamiltonian is time dependent or rather in case of non isolated systems, or in case of non stationary interactions between different bodies.The attempt to model a free falling body in a gravitational field for GRT seems impossible.

GRT has been tested only for static or stationary systems where there is not a net exchange of energy (excluding gravitational radiation)

Don't we need another GRAVITATIONAL THEORY which includes the results give by GRT in order to explain with a better accuracy the simple phenomenon like the free falling of a mass in a gravitational field?