[Richard777 (OP)]

A vector has magnitude, and direction. The vector includes a frame of reference (orthogonal unit vectors), scalar components, and is also associated with “directional angles”.

A “dynamic vector” changes from an initial state to a final state. The vector has a subscript indicating the “current state”. The components also have a subscript, indicating the same current state.

The magnitude and the direction both change, however the frame of reference does not change. The unit vectors do not have a subscript. The “observation” is fixed and the vector is variable.

Change is represented as the difference between final components and initial components and is associated with “components of difference” having a new subscript.

If the frame of reference does not change, then there is no need for a tensor. Can a dynamic vector substitute for a tensor?

If special conditions are true, then the components of difference associated with a dynamic vector of acceleration will give the Schwarzschild metric.