Can a “Schwarzschild Vector” give the Schwarzschild metric?

[chemguy]

A vector of “incremental distance” (in 4D) has a change of direction with no change of magnitude.

A component of incremental distance may be associated with a component of acceleration.

This is the “Schwarzschild vector”.

Simple transformation should give the Schwarzschild metric.31 The Schwarzschild Vector.pdf

 

 

[Bufofrog]

3 hours ago, chemguy said:

A vector of “incremental distance” (in 4D) has a change of direction with no change of magnitude

OK.

3 hours ago, chemguy said:

A component of incremental distance may be associated with a component of acceleration.

What is this association?

Why do you call it the Schwarzschild Vector?