L E C T U R E S A T U N I V E R S I T Y O F B U E N O S A I R E S 9 6 3 While in Newton’s theory, he added, there is just one gravitational potential, in the gen- eral theory there are ten. There are also ten equations, therefore, that define them. The latter, and thus the former, are reduced to six—he said—through four equations that connect them (for reasons given above)…. Furthermore, Dr. Einstein said, since as we have seen in the theory of the electromagnet- ic field, instead of the density of matter, we have the energetic tensor made up of the six components of the pressures and tensions that are stimulated in matter because of de- formations: the three quantities of movement and the density of energy or of mass. Since they are identified in relativity, it seems plausible to write the following as gravitational equations: (1) The second term—Dr. Einstein said—is reduced to the product of the gravitational con- stant κ times the density of the matter when the first term is reduced to Laplace’s equa- tion from ordinary mechanics. This must be required of all equations that seek to define the gravitational field, he added, since Newton’s equations describe reality in a first and subtle attempt. The reduction of (1) to Poisson’s equation, which we have just finished discussing, is produced when there is no movement within the matter, since in that case the tensions and quantities of movement disappear.) The equations in (1) cannot be taken as gravitational equations—Dr. Einstein said— even though they satisfy the conditions stipulated, in that they do not conform to some of the invariance characters demanded by the principle of relativity, for which reason it is nec- essary to replace them with others. He defined such others as follows: (2) where R is the sum of the products . Those equations, he said, possess the proper- ties of (1) and of other invariant equations, since the divergence of the first term is zero. Those are, he said, the most general and only equations that can be calculated in an ex- clusively mathematical way and that satisfy the required conditions we have mentioned. If they do not represent reality, there are no others. Determinants of g Values The problem of determining gravitational potentials, Dr. Einstein continued, is a daunt- ing one. They are defined, he said, by ten equations, each of which contains an infinitude of terms, some of them made up. However, the solution becomes much simpler, since we can give ourselves four of the equations for reasons provided earlier. By choosing those four equations arbitrarily, we are merely establishing at will a certain system of Gaussian coordinates, which we have every right to do because of the principle of general relativity itself. Tμν Rμν gTμν = Rμν Rμν 1 2 --gμνR - – kTμν = gμνRμν