Einstein most basic field equations in Tensor form gives the curvature R of space time on the left hand side and the momentum energy density tensor T on the right hand side. What happens if one takes the gradient of both sides. That is because the gradient of energy density is acceleration. For example pressure is energy density and the gradient of pressure in fluids is a driver of flow. The same can be said for the flow of electrons in electric currents etc.

On the left hand side, the gradient of the curvature is a second derivative of the path of a particle. This appears to transform the field equations to the statement that acceleration is the result of energy gradient in the case of gravity too. This seems to remove the mystery in imagining the space time curvature which is the most unintuitive part of GR. Gravity force becomes the negative gradient of energy density like all other types of motion.