stands a purely geometrical quantity (the Ricci scalar is the trace of the Ricci tensor, which is itself a kind of trace of the fourth rank Riemann curvature tensor), and on the right hand stands a purely physical quantity, the trace of the stress–energy tensor. Einstein gleefully pointed out that this equation now takes the form which he had earlier proposed with von Laue, and gives a concrete example of a class of theories which he had studied with Grossmann. Some time later, Hermann Weyl introduced the Weyl curvature tensor , which measures the deviation of a Lorentzian manifold from being conformally flat, i.e. with metric tensor having the form of the product of some scalar function with the metric tensor of flat spacetime. This is exactly the special form of the metric proposed in Nordström's second theory, so the entire content of this theory can be summarized in the following two equations: Features of Nordström's theory Einstein was attracted to Nordström's second theory by its simplicity. The vacuum field equations in Nordström's theory are simply We can immediately write down the general vacuum solution in Nordström's theory: where and is the line element for flat spacetime in any convenient coordinate chart (such as cylindrical, polar spherical, or double null coordinates), and where is the ordinary wave operator on flat spacetime (expressed in cylindrical, polar spherical, or double null coordinates, respectively). But the general solution of the ordinary three-dimensional wave equation is well known, and can be given rather explicit form. Specifically, for certain charts such as cylindrical or polar spherical charts on flat spacetime (which induce corresponding charts on our curved Lorentzian manifold), we can write the general solution in terms of a power series, and we can write the general solution of certain Cauchy problems in the manner familiar from the Lienard-Wiechert potentials in electromagnetism. In any solution to Nordström's field equations (vacuum or otherwise), if we consider as controlling a conformal perturbation from flat spacetime, then to first order in we have Thus, in the weak field approximation, we can identify with the Newtonian gravitational potential, and we can regard it as controlling a small conformal perturbation from a flat spacetime background. In any metric theory of gravitation, all gravitational effects arise from the curvature of the metric. In a spacetime model in Nordström's theory (but not in general relativity), this depends only on the trace of