Only Weak Gravity (1/3)
A potential that only applies to gravity not EM will have a diagonal field strength tensor.
 The sign of the spring constant k does not effect solving the field equations.

The sign of the spring constant k does change the derivative of the potential
to first order in k.

Therefore a potential that only has derivatives along the diagonal can be
constructed from two potentials that differ by string constants that either
constructively interfere to create a nonzero derivative, or destructively
interfere to eliminate a derivative.