way to the introduction of a more comprehensive theory, in which it lives on as a limiting case.
In the example of the transmission of light just dealt with, we have seen that the general theory of relativity enables us to derive theoretically the influence of a gravitational field on the course of natural processes, the laws of which are already known when a gravitational field is absent. But the most attractive problem, to the solution of which the general theory of relativity supplies the key, concerns the investigation of the laws satisfied by the gravitational field itself. Let us consider this for a moment.
We are acquainted with space-time domains which behave (approximately) in a “Galileian” fashion under suitable choice of reference-body, i.e. domains in which gravitational fields are absent. If we now refer such a domain to a reference-body possessing any kind of motion, then relative to there exists a gravitational field which is variable with respect to space and time.[1] The character of this field will of course depend on the motion chosen for . According to the general theory of relativity, the general law of the gravitational field must be satisfied for all gravitational fields obtainable in this way. Even though by no means all gravitational fields
- ↑ This follows from a generalisation of the discussion in Section XX.
