Does space-time cause time dilation at relativistic speeds?

I'm trying to understand the concept of the space-time continuum and it's effect on time dilation but am having difficulty with parts of it. To me there seems to be two separate components to time dilation...

1. Space-time is warped by mass (the stronger the gravitational field the slower time goes).

2. Time dilation at relativistic speeds (the faster you go the slower time goes).

I understand that space-time is effected by mass and this makes sense. But are we talking about the same warping of space-time when travelling at relativistic speeds (e.g. is the warping proportional to the speed)?

Specifically my confusion arises if we consider a spaceship travelling at say 50% the speed of light. Time dilation will have some effect here and time will travel slower on the spaceship. That is fine but is that due to space-time? E.g.

• Is space-time warped around the spaceship?
• Is it dragged along with the spaceship as it moves?
• What is the boundary? Is there time dilation within the spaceship which instantly changes to zero time dilation at the outside boundary of the spaceship or is there a gradient from outside to inside?
• If we consider a move complex shaped spaceship that is rotating (say a hexagonal mesh sphere with hollow inside) it seems impossible that space-time could be dragged along by this as it would be cutting its way through space-time or making a swirling mess of it.

I find it hard to understand how space-time can 'follow' a moving spaceship through space. It seems that #1 & #2 above are two separate things (e.g. both aren't caused by space-time). Is this correct? Or is space-time dragged along with a moving spaceship?

Note: I understand that the spaceship has mass and this will warp space-time to a small degree (and cause a tiny amount of time dilation) but am more interested in the time dilation caused by the spaceships speed (and the relationship between the speed, time dilation and space-time).

• There are two difference sources for time dilation, gravity and speed. The speeding spaceship doesn't warp space time or drag anything with it. Each atom is experiencing time dilation, so it doesn't matter what the shape of the spaceship is. Commented Apr 10, 2015 at 23:33