To discover the relativistic field equations for gravitation we begin with a linear approximation for the gravitational field, that is, we neglect the effects of the gravitational field on itself. Of course, if Newton’s principle of equivalence (mI = mG) is to hold as an exact statement, gravitational energy must gravitate, and the exact field equations must be nonlinear. Although it is true that some of the most spectacular results of gravitational theory depend in a crucial way on the nonlinearity of the field equations, almost all of the results that have been the subject of experimental investigation can be described by the linear approximation. For example, the deflection of light, the time delay of light, gravitational time dilation, gravitational lensing, and gravitational radiation emerge from the linear approximation. Furthermore, this approximation applies to all phenomena that lie in the region of overlap between Newton’s and Einstein’s theories.

Most discussions of gravitational theory begin by postulating that spacetime is curved and from there proceed to formulate the nonlinear equations that govern the curved spacetime geometry. The linear approximation then arises in the end from the full nonlinear equations. The great disadvantage of this approach is that it never makes clear just why anybody would entertain the preposterous notion that our beautiful flat spacetime should be curved, bent, and deformed.