In Part I of his book Principles of Relativity Physics, Academic Press, New York, London, 1967, James L. Anderson, at pages 1-101, gives an account of the methods of tensors and covariant derivatives and the like.

In Part III, “Dynamical Space-time Theories”, Chapter 10, “Foundations of General Relativity”, Section 10.4, “The Einstein Field Equations”, at page 347-348, Anderson tells us that “Any system of local differential equations will in general admit a large number of physically inequivalent solutions. To decide which one of these solutions are actually realized in nature, it is customary to supplement the equations with boundary conditions.” Anderson then notes that Einstein “suggested that one should not give boundary conditions to supplement the field equations [of his ‘general theory of relativity’], but rather should require that all solutions lead to geometries that are spatially closed.” Anderson goes on to say that “The question of boundary conditions is still to a large extent an open one.”

Although Anderson does not draw the following conclusion, and does not seem to even consider it, these remarks of his are in effect a polite way of saying that Einstein’s “general theory of relativity” is indefinite, ambiguous, or non-specific as to some physical predictions that might be asked of it, and is therefore in those respects not empirically falsifiable. It is only as to differential relations that it is falsifiable.

Christopher