I hope someone knowledgeable is still reading comments this late: I was thinking about this last night. How does this fit into GR? I understand how it fits i

I hope someone knowledgeable is still reading comments this late: I was thinking about this last night. How does this fit into GR? I understand how it fits into SR, but in GR space is just curved. Unlike velocity time dilation, under Einstein space isn't moving. In GR it's the curve that's "equal" to gamma, the dilation factor in SR. This is evident where escape velocity (root((2GM)/r)) replaces the (v^2) term in the Lorentz factor to give gravitational time dilation in the Schwarzschild solution (t' = t(root(1-(2GM)/(rc^2))). Mind you, I've always thought everything is moving at c through spacetime, but I understood that from SR. I just don't see how it fits with GR.