ON THE PHYSICAL SIGNIFICANCE OF COORDINATES AND THE SOLUTIONS OF THE FIELD EQUATIONS IN EINSTEIN'S THEORY OF GRAVITATION

The present paper brings up the physical significance of coordinates in relation to theboundary value conditions on the gravitational potentials which satisfy Einstein’s field equa-tions of gravitation. Owing to the Bianchi identity these field equations have to be supple-mented by the harmonic condition in order to render their solutions definite. The componentg00 of the metric tensor gμv with the exception of the infinite plane, should become theNewtonian potential in certain region outside the gravitating body under consideration. Weuse the above conditions to find the solutions of the static fields of the spherical mass andthe infinite rod with uniform linear density of matter. For the infinite plane with uniformsurface distribution of matter the above condition on g00 is a necessary consequence and theprinciple of equivalence is then adopted to make the solution definite from which Galileo ’s lawof falling bodies is derived. The analysis of this result shows, as an example, the physicalsignificance of coordinates. This program can be applied to solving general problems ofgravitation in Einstein’s theory.