[Richard777 (OP)]

Acceleration may be represented in different forms;
as a scalar
as a vector
as a tensor
A vector is four dimensional. The tensor is rank two.
Various forms of acceleration may be related as ratios.
A change of basis may also include a ratio of unit vectors.
Can ratios of form and basis give the Reissner-Nordström metric?
See attachment.

[PmbPhy]

Acceleration may be represented in different forms;
as a scalar
as a vector
as a tensor
A vector is four dimensional. The tensor is rank two.

Only 4-acceleration is a 4-vector. 3-acceleration is a 3-vectgor. And acceleration is a rank-1 vector, not a scalar or a tensor of higher rank.

Various forms of acceleration may be related as ratios.
A change of basis may also include a ratio of unit vectors.

Those statements are wrong. You didn't justify any of your claims here.

Can ratios of form and basis give the Reissner-Nordström metric?

No.