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The Newtonian gravitation theory is generalized to an inhomogeneous wave equation for a tensor gravitational potential in Euclidean space-time by invoking the special relativity postulates of Lorentz invariance and equivalence of mass and energy. Under the assumption of Lagrangian derivability, this is found to lead uniquely to the generally covariant field theories (including the general relativity theory) augmented by four auxiliary conditions. Appendices treat the general definition of the energy tensor, and an empirically disqualified special relativistic scalar generalization of the Newtonian theory.
Robert H. Kraichnan (Sun,) studied this question.