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”, in his introduction to Chapter 10, “Foundations of General Relativity”, at pages 329-330, Anderson tells us about Einstein’s assumptions for his “general theory of relativity”. Anderson writes “…Einstein succeeded in actually eliminating geometry from the space-time description of physical systems …” Anderson goes on to clarify “While it is still convenient to use geometrical terminology in discussing the general theory, nowhere is it necessary to use the gravitational field tensor g mu nu explicitly as a metric (for example, in an expression for the distance between two neighbouring points).”

Christopher