>Dear Readers: I apologize; there's one point in this article that's not quite right and ought to be clarified. Namely, when I said that a spaceship traveling exponentially close to the speed of light would collapse to a black hole: that's only true because, when the spaceship inevitably collided with some interstellar particle, the energy in the center-of-momentum rest frame would be exponential. A spaceship in a theoretical vacuum could get arbitrarily close to the speed of light without collapsing.
>However, it's important to understand that this doesn't change the computational situation in any important way. It's still true that, to accelerate exponentially close to the speed of light, you need an exponential amount of energy! And therefore, it will take you exponential time to accelerate to such a speed---unless your fuel tank (or whatever else is providing your energy) is exponentially concentrated, in which case it will exceed the Schwarzschild limit and indeed collapse to a black hole.
>However, it's important to understand that this doesn't change the computational situation in any important way. It's still true that, to accelerate exponentially close to the speed of light, you need an exponential amount of energy! And therefore, it will take you exponential time to accelerate to such a speed---unless your fuel tank (or whatever else is providing your energy) is exponentially concentrated, in which case it will exceed the Schwarzschild limit and indeed collapse to a black hole.