The curvature is thus less thorough, since
vanishes.
In regions outside matter, where no electromagnetic fields are present, the curvature is still less pronounced, for there
, however, vanishes only for points infinitely distant from matter (in the hypothesis of the infinite universe).
In absolutely free space, remote from matter and where there is no electromagnetic energy, all the tensors and invariants vanish.
We thus find that there exists a progressive curvature of space-time as we pass from empty space-time far removed from all matter and energy to empty space-time in the neighbourhood of matter, then to regions where there are electromagnetic fields but no matter, and finally to regions filled with matter or electrons. If we regard the successive gradations of curvature of space-time as corresponding to successive grades of materialisation, starting from emptiness, we must place electromagnetic fields, or loose energy, at a stage of materialisation preceding that of matter proper, or bound energy.
Still another discovery which Einstein was able to deduce from his gravitational equations refers to the propagation of a gravitational force. Classical science had held to the view that gravitation must be propagated with a speed much greater than light, perhaps even with infinite speed. But Einstein, by integrating the equations of gravitation, proved that in a weak field gravitational waves would be propagated with the speed of light. In a strong field, of course, the presence of the field itself would influence the speed of propagation of the waves, and the problem would assume much greater complexity.