LextheNonTrivial

I agree that the mission would necessarily take a very long time in the Earth's rest frame. But remember that in SR, rapidity (the rate of distance in someone else's frame travelled with respect to your time) can be arbitrarily large. If we could accelerate a ship to very near light speed over a short enough time, without killing the crew, we could get them there within 5-6 years of their time, easy. It's not at all the same thing of course, and everyone they knew on Earth would be dead, most likely along with human civilization and the Earth itself... But the colony itself should be fine so long as they didn't depend on interaction with the Earth.

You seem to have misread that a bit- I was trying to point out that the scalar curvature is proportional to the invariant rest mass, not relativistic mass. The whole idea behind using a scalar equation is that they don't depend on the metric/frame/coords used. Going faster doesn't have any affect on how much scalar curvature something causes; at best the curvature is just redistributed through spacetime.

Mathematically: It shows that the Ricci scalar is proportional to the rest mass density- after all scalar equations can't reference energy or momentum as those concepts are undefined without a metric. It's relevant to the question about whether gravity is proportional to relativistic mass or rest mass. Philosophically: I don't know, curiosty?

How about this for those familiar with only special relativity... Simply consider the Sun from a frame moving at, say, c - .0003 m/s , so that its mass increases and its Schwarzschild radius is greater than its physical radius (by a factor of about 5 at that speed, if my maths are good). It's a black hole now. As a black hole is a black hole in any frame, we know that the Sun is actually a black hole in its own rest frame, regardless of appearances... In other words, no- gravity isn't simply proportional to relativistic mass. Yes, I know this is technically, or even wildly, inaccurate, given GR. I feel it's a fun refutation nonetheless. @K^2 : If you're familiar enough with GR maths, try contracting indeces on Einsteins equations (by way of a locally Minkowskian metric). It's kind of pertinent to this.