Equivalence principle & nonlinearity

[Thrice]

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.

 

[MeJennifer]

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".