Constant acceleration equal to 1 g in which frame?

Not in the station's frame. Why not? Because v=at would exceed the speed of light c in time t = c/g = 3*10^7 seconds = 1 year.

So it must be a constant acceleration of 1 g in the frame of either ship. This is the "proper" or "felt" acceleration. (Just as the time experienced by the ships' crews is the proper time.) This way, the crews will experience an artificial "gravity" similar to Earth's real gravity.

http://www.xs4all.nl/~johanw/PhysFAQ/Relativity/SR/rocket.html

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