In fact I don't even need to spin around, just being on the spinning earth is good enough.
Suppose I look out into space at the nearest star, Alpha Centauri, approximately 4 light years away. Working from the gravity accelerated frame of reference that I occupy on the surface of the earth, th star appears to go around the earth in one day, travelling a distance of $2*\pi*4$ or roughly 24 light years - in a day.
What I am really getting at, is that relativity tells us all frames of reference are valid, as well as that things cannot travel faster than light. But from this particular frame of reference, that would not seem to be true.
This accelerated, rotating frame of reference can be described as equivalent to some other frame by general relativity, so I think it is valid to look at it from different frames of reference.
Does this imply that the theory of general relativity does not place an upper bound of the speed of light on velocity?