’s, namely, the time one,
.[94]
According to Einstein’s views, therefore, the expression of the gravitational potential distribution in the interior of matter will be given by an equation between some complicated expression connecting the ten
’s at every point and at neighbouring points, and some quantity representing the characteristics of matter at every point. This equation will then constitute Einstein’s law of gravitation in the interior of matter, and will represent the Einsteinian substitute for Poisson’s classical equation.
Now Poisson’s equation was an equation between two invariants in space. Einstein’s law, on the other hand, in accordance with the requirements that must be satisfied by all general laws in the space-time theory, will have to be an equation between invariants or tensors in space-time. By analogy with Poisson’s equation we see that the left-hand side of Einstein’s law will be a space-time invariant or tensor which will represent the potential distribution, or
-distribution, from point to point, while the second side will be given by an invariant or a tensor representing matter.
A tensor representative of matter and describing it fully had already been discovered by Einstein. It was a second-order symmetrical tensor generally written