[Galileo1564 (OP)]

Just a novice trying to get an idea for how the EFE's work in general. If the stress energy tensor (right hand side) "vanishes in a vacuum", how is the vacuum above the surface of the earth described by the left hand side (geometry part) of the EFE's?

I think there is still curvature above the surface of the earth, and even if the curvature tensor is extremely small and the Einstein tensor approaches Newtonian, is seems like the Einstein tensor does not vanish above the surface of the earth, even though the stress energy tensor does.

So the equations are shown with the left hand side equated to the right hand side.
The right hand side vanishes in a vacuum.
There is a vacuum above the earth.
But there is still gravity above the earth. so the left hand side must still have non-vanishing values.
Yet the left hand side equals the right hand side which vanishes.

[Halc]

Just a novice trying to get an idea for how the EFE's work in general. If the stress energy tensor (right hand side) "vanishes in a vacuum", how is the vacuum above the surface of the earth described by the left hand side (geometry part) of the EFE's?

Earth is not a vacuum.  The vacuum solution to the field equations means a vacuum everywhere, not just locally.

I think there is still curvature above the surface of the earth, and even if the curvature tensor is extremely small and the Einstein tensor approaches Newtonian, is seems like the Einstein tensor does not vanish above the surface of the earth, even though the stress energy tensor does.

Yes, else orbits would not follow geodesics.

[Galileo1564 (OP)]

Earth is not a vacuum.  The vacuum solution to the field equations means a vacuum everywhere, not just locally.

Ahh. So when they are talking about stress energy tensor vanishing in a vacuum, they mean in a vacuum far removed from any gravitational bodies, not the vacuum above the earth.

When I say "they", I mean when I see videos of people "deriving" the EFE's etc., they sometimes start with saying that the stress energy tensor in a vacuum vanishes, and then they carry on with their calculations.  That's confusing because aren't we usually interested in the EFE's of areas of space near massive bodies, not far removed? I never see them say something like "here is the stress energy tensor representing the energy of the earth" and then doing their calculations.

So what is important about vacuum SET when discussing EFE's? Is it just a starting point for calculating EFE's of massive bodies, and then later the energy of the massive body is to be added in?