What you might be missing is time. Things don’t really “sit still” in spacetime—everything is always moving through time, but things that are moving fast through space are moving slower through time—it’s like you have just one speed, but you can point it “out of time” and “into space.”
When you travel through a curved spacetime, “sitting still” still means moving forward in the time direction. It’s not like the curvature due to gravity creates a potential well that you “fall down.” It’s more like you’re one of those stunt motorcyclists driving around the inside of a steel cage, constantly whizzing forward in a locally straight line, but changing what direction you’re pointing due to the curvature of space.
What you might be missing is time. Things don’t really “sit still” in spacetime—everything is always moving through time, but things that are moving fast through space are moving slower through time—it’s like you have just one speed, but you can point it “out of time” and “into space.”
When you travel through a curved spacetime, “sitting still” still means moving forward in the time direction. It’s not like the curvature due to gravity creates a potential well that you “fall down.” It’s more like you’re one of those stunt motorcyclists driving around the inside of a steel cage, constantly whizzing forward in a locally straight line, but changing what direction you’re pointing due to the curvature of space.