[Richard777 (OP)]

Can space be represented as a “structure” of three “dimension vectors”?

The vectors have a common origin and are “connected” by sharing common components. The connected vectors represent space.

Assume that matter and motion deform space. Characteristics of matter and motion are represented as “length scales”. The length scales are associated with mass, charge, and rotation. A ratio of length scale represents distortion. Deformation is represented as a ratio of incremental length. Assume deformation is equal to distortion.
 
Five “rules” may govern the structure and deformation “incremental space”.

If vector components are suitably defined then a “deformal spatial equation” will give the Kerr-Newman metric. If charge and rotation do not apply, then the Kerr-Newman metric will reduce to the Schwarzschild metric. Empty incremental space is represented as the Minkowski metric.

Can space be represented as a “structure” of three “dimension vectors” ?

[evan_au]

Can space be represented as a “structure” of three “dimension vectors” ?

Position in space can be represented as three dimensions of length (relative to some origin).

The length scales are associated with mass, charge, and rotation.

Length scales are associated with meters.
- Mass is associated with Kilograms.
- Charge is associated with Coulombs
- Rotation is associated with angular momentum
- So, no, mass charge and rotation cannot be associated with length scales.

Kerr-Newman metric....Schwarzschild metric...

These metrics are associated with black holes.

And it is true (so far as we know) that the only things you can know about a black hole are its mass, angular momentum & charge. But angular momentum has both magnitude & direction, so it inherently contains several dimensions.

So you could represent the characteristics of a black hole by these five(?) dimensions (but they are still not length dimensions).

Can (a black hole) be represented as a “structure” of three “dimension vectors” ?

If you had any interest in finding this black hole again, then you would also want to record it's position in 3 dimensions (relative to some coordinate system).

If you had any interest in finding this black hole in the near future, then you would also want to record it's velocity in 3 dimensions (relative to some coordinate system).

By my count, you would want to record about 11 dimensions of information about a black hole.

If you had any interest in finding this black hole in the distant future, then you would also want to record similar information about all masses in the region, so you can estimate the future distortions of space.

But most objects in the universe are more complex than a black hole, so you would need to record more information about them - for example the distribution of mass (which deforms space) is more complex for a planet, a star or a galaxy.

[PmbPhy]

Can space be represented as a “structure” of three “dimension vectors” ?

I agree. To put a fine point on it the dimension of a manifold (aka "space") is how many numbers i takes to uniquely define a point in a space. That doesn't mean that it takes three distances. Consider spherical coordinates. One number measures a distance from the origin while two represent angles.

Length scales are associated with meters.

Not always true here in the US where things are often measured in miles, etc.

Kerr-Newman metric....Schwarzschild metric...

These metrics are associated with black holes.

The Schwarzschild metric is used for more than that. It describes stars and planets too.

[jeffreyH]

You beat me to it Pete. 

[yor_on]

It intrigues me Richard, but don't you need to consider relative motion and accelerations in your proposal too? You write "Assume that matter and motion deform space. Characteristics of matter and motion are represented as “length scales”. The length scales are associated with mass, charge, and rotation."

seems to me that 'motion' has a lot to do with at what length scales you define other objects to be relative yourself?

Ahh okay. You do look at it and from there go to mass charge and rotation?
But I don't get how you leave 'motion' for it?

And what does this mean? "  Assume deformation is equal to distortion. " Distortion of what? A vacuum? Are you thinking of it as a actual contraction or as a optical?