# Does a relativistic rocket lead to time dilation in the space surrounding the rocket?

This question was asked a few years ago, but I'm looking for more complete answers. And of course I recognize that any dilation effects would be extremely small. If a rocket is traveling at relativistic speeds, then certainly there is time dilation inside the rocket (from our frame on Earth). But what of the space surrounding the rocket?

1. Is there any time dilation in the space surrounding the rocket? (I'm thinking only of time dilation caused by the speed and not the mass of the rocket.)
2. Is there any warping of spacetime in that space outside of the rocket, and would there be any frame dragging?
3. If the rocket is accelerating, then would it create gravitational waves in the space surrounding it and emanating outwards? (These waves could be a function of its mass, or its speed, or both).
4. If the answer to the above two questions is "no", then is the boundary between slow time and fast time literally the outer wall of the rocket?
• At the level of special relativity, time dilation is associated with moving objects. If it isn't moving, there isn't time dilation. You can't assign "slow time" or "fast time" to the empty space right outside the rocket because there isn't anything there. A moving object (with respect to the lab frame), either inside or outside the rocket, has time dilation (in the lab frame), and a nonmoving object, either inside or outside the rocket, doesn't. Apr 6, 2020 at 20:31
• @knzhou I guess I asking that if the rocket flew right past a clock. Then for an instant the clock would (might) be inside the influence of the rocket. So would the clock slow down, just for that instant when the rocket was flying past? Apr 6, 2020 at 20:36
• Certainly, but it depends on a lot of details, such as the mass of the rocket, its shape, and its full trajectory, while the good ol' special relativistic time dilation depends on absolutely nothing but the speed of the clock. Apr 6, 2020 at 20:40
• Excellent question, and intuitive, yes the rocket with its relativistic mass will bend spacetime much more than the rocket in rest. Apr 7, 2020 at 9:16
• @HolgerFiedler Your answer is key to my theories. Unfortunately in a paper it's probably not too good to reference a comment in the Physics Stack Exchange. Can you point me to a reference about how the rocket will bend the surrounding spacetime? Apr 4, 2022 at 19:26