We mentioned, when discussing tensors, that several such invariants exist, but that the simplest of all was represented by the Gaussian curvature
. To this
we may add any scalar or number
without modifying its invariance, since numbers are, of course, invariants. Hence, the simplest expression for the function of action of the metrical field is obtained by writing it:
. This was, indeed, the expression selected by Einstein.[125]
From now on, it is a mere question of mathematics (calculus of variations) to express the stationary condition of the total action. As a result, we obtain Einstein’s law of space-time curvature, inside and outside of matter; that is to say, Einstein’s law of gravitation. According to whether we assume that