In comparison with STR, which is a static theory of the kinematic structures of Minkowskian spacetime, GTR as a dynamical theory of the geometrical structures of spacetime is essentially a theory of gravitational fields. The first step in the transition from STR to GTR, as we discussed in section 3.4, was the formulation of EP, through which the inertial structures of the relative spaces of the uniformly accelerated frames of reference can be represented by static homogeneous gravitational fields. The next step was to apply the idea of EP to uniformly rotating rigid systems. Then Einstein (1912a) found that the presence of the resulting stationary gravitational fields invalidated the Euclidean geometry. In a manner characteristic of his style of theorizing, Einstein (with Grossmann, 1913) immediately generalized this result and concluded that the presence of a gravitational field generally required a non-Euclidean geometry, and that the gravitational field could be mathematically described by a four-dimensional Riemannian metric tensor gμv (section 4.1). With the discovery of the generally covariant field equations satisfied by gμv, Einstein (1915a–d) completed his formulation of GTR.

It is tempting to interpret GTR as a geometrization of gravity. But Einstein's interpretation was different. For him, ‘the general theory of relativity formed the last step in the development of the programme of the field theory … Inertia, gravitation, and the metrical behaviour of bodies and clocks were reduced to a single field quality’ (1927).