[Richard777 (OP)]

If the Schwarzschild metric is simply obtained from the Einstein Field Equation, then the Christoffel symbols may not be required.

The product of a tensor and a vector gives a different vector.
Tnr = cvn 
Where;      
Tn is a tensor of acceleration
c is a scalar of velocity (the light constant)
vn is a velocity vector
r is a location vector

The EFE is an equation containing scalars and Tensors.
If a vector multiplies with all terms of the EFE, the result is an equation of scalars and vectors.
If another vector multiplies across the modified EFE (inner product) the result is an equation of scalars and cosines.
The Schwarzschild metric may be obtained from the second modified equation.
Is this procedure valid?

[Richard777 (OP)]

Is there an Einstein Length (R_E)?
Similar in concept to Plank Length.

    R_E = (hc)^1/2

It may be included in the "Einstein gravitational constant" (K_E)
Is this length valid ?