Vacuum and non-vacuum regions, dust and fluids

[Passionflower]

In GR there is made a clear distinction between a vacuum region and a non-vacuum region as one is handled by the Ricci tensor and the other by the Weyl tensor.

But is reality so black and white? And when do we realistically talk about dust and when about fluid?

So the inside of an average star, what is the percentage of vacuum?

 

[Bill_K]

In a vacuum region the Ricci tensor is zero and the Weyl tensor is nonzero. In nonvacuum, both Ricci and Weyl tensors are nonzero.

is reality so black and white?

We work in reasonable approximations, and often pretend that matter is continuous, not made up of atoms in random motion. We then make use of averaged quantities, including an averaged Ricci tensor.

And when do we realistically talk about dust and when about fluid?

"Dust" refers to matter in which the pressure is negligible compared to the energy density.

So the inside of an average star, what is the percentage of vacuum?

What percentage of the air in your room is vacuum? The answer depends on how fine a scale you're interested in. You can count the space between atoms as vacuum. Or you can even say that the interior of each atom is mostly vacuum.