Why is there gravity at a distance?

[Khashishi]

I'm trying to understand the Einstein field equations. My rough understanding is that the local curvature is due to the local stress-energy. Ok, a mass curves space...I get it. But, isn't space curved in the vacuum surrounding a mass? I mean, light is bent by a star even at some distance away from the star. Isn't the stress-energy zero outside the star?

Does this have something to do with the Weyl curvature which isn't included in the field equations?

 

[Dale]

Remember that there are a few different curvature tensors. The Ricci curvature tensor will be 0 in the vacuum surrounding a mass (per the EFE), but the Riemann curvature tensor may in general be non-zero.

 

[Matterwave]

I think there's a very nice analogy to E&M here. Even far away from the sources of the fields (the charges and currents), the fields themselves can exist. For example, in a static situation outside a charge distribution:

\nabla \cdot \vec{E} = 0

\nabla \times \vec{E} = 0

But it doesn't mean there is no electric field there. One has to consider boundary conditions. Similarly, Einstein's equations are second order differential equations, so even without a local source, boundary conditions can induce curvature.