The field energy density /gravitational energy density is missing in General relativity but in Newtonian gravitation, it is present and negative as expected.

As stated by Penrose not very accurately, about potential energy

"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 which makes the total energy, and therefore the total mass, smaller than it would be if they are far apart.  Ignoring much tinier energy effects, such 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)."

As a matter of fact what is negative is the binding energy which is localizable... what is not localizable is the potential energy.

There is substantial a difference between gravitational energy which is negative in Newtonian Gravitation and is a sort of BINDING ENERGY and Potential energy which is positive since it is "given" to the system of attracting masses.

It is undisputed that there is no room at all for a potential energy density in gravitation since it is not determinable from where such energy comes from, although it cannot be part of the "gravitational field"...

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