In SR, we may choose any inertial observer and his reference frame at which he is at rest, and other observers are movin wrt to him. All the moving observers 'slice' spacetime in a different way than the observer at rest, at different angles relative to his simultaneity surfaces. This is all flat space time nature. My question is, how does this translate to GR and curved space time? How do different observers slice curved space time and what does it look like compared to SR. I know that we have hovering observers and relative to them clocks far away form gravity run faster etc. What about moving observers (free falling observers) and the simultaneity slicing while gravitational time dilation is present? And please don't say that any coordinate system is acceptable, I know that, and my question is basically the comparision in simultaneity differences between moving and static observers in SR and GR. Thanks in advance.