I think that; “gravitational field energy” is an attempt to explain something that is not understood.
The meaning of the word “energy” should be clarified. How do you define the word “energy?” As far as I am concerned “energy” is always kinetic. Potential is simply that; POTENTIAL for (kinetic) energy.
Back in the early 1950’s I purchased a booklet that was titled ENERGY, In that booklet there was a very simple illustration of the difference between the potential and kinetic forms of energy. There was a illustration of a swinging pendulum, when the pendulum was stationery in the highest position, then the potential for the kinetic form of energy was highest and when the pendulums swing was at the lowest point then the kinetic form of energy was highest and the potential form was at its lowest. I suspect that this type of oscillation between the kinetic and potential form of motion is what exists in all types of mass including all photons.
So, what is it that is actually moving, and how did it come into existence,
All scientists seem to agree that space, mass, and energy exist. According to Einstein, mass always contains energy. If you convert mass totally into energy then the mass has the maximum velocity. For mass to contain energy, and that energy is basically motion, then there must be space within the mass, otherwise motion could not exist there.
There are three essential ingredients that makes up mass,they are, space, motion, and something that moves. Each of the ingredients can be increased or decreased but never separated, therefore mass can be considered as a “trinity.”
How did mass come into existence: There are a very old books with writings that explain the story very well, but since the scientific community can not cope with such information at this moment in time, I will leave that explanation out for now.
Suffice to say that if someone cannot accept the act of creation, then that person will not accept the information.