[Richard777 (OP)]

Each point in the continuum may be associated with a vector and a co-vector (vector pair).

Both represent deformation of the continuum. One is a displacement vector, representing the displacement of a point in the continuum due to stress. The co-vector (incremental vector) represents a gradient of displacement.

Two frames of reference are required. The origin of each frame is a point in the continuum. This gives four “field vectors” (a vector pair at each origin).

A field is defined if the components of the vector pairs are related in some manner. The vector components (and geometries) are related by “field rules”.

If the vector types and the field rules are suitably defined, then the Schwarzschild metric may be simply obtained.

Can the Schwarzschild metric be simply derived in this manner?

[jeffreyH]

The following wikipedia article may be useful.

https://en.m.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution

The metric has an inbuilt symmetry due to its nature. I haven't examined your pdf yet so cannot comment further.