Equivalence principle & nonlinearity

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How does nonlinearity of the gravitational field equations follow from the equivalence principle? I remember hearing a handwaving example of this & I'm interested in more details.
 

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How does nonlinearity of the gravitational field equations follow from the equivalence principle? I remember hearing a handwaving example of this & I'm interested in more details.
The closer a collection of masses come together the less the sum of their inertial masses becomes. Hence, to maintain equivalence the total gravitational mass has to couple to this increasing "defecit".
 

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