Nearly every mention of time, distance, or speed is deeply flawed. While I
somewhat enjoyed the story while I listened to it, when it was over and I started thinking the numbers involved I got more and more annoyed, to the point that it is now 15 hours later and the first thing I'm doing with my work day is posting about it.
As a very simple example, it should have taken our "hero" at least 56hours to change his speed by .1c. And that is a face-melting constant 15g acceleration. There are lots of other examples of horrible math but just sharing that one makes me feel better. If the author had left off any mention of speed or distance, it would have been easier to take (and then we would have merely had problems with characters making awful decisions.)
For those that are interested in the math--
c = 300,000,000 meters per second (okay, it is actually 299,792,458 m/s but close enough)
So .1c = 30,000,000 m/s
the equation for a simple change in velocity is V = a * t. (Change in velocity equals acceleration multiplied by time.)
I will assume a constant acceleration of 15g (which is crazily high, but seemingly tolerable by human beings
http://en.wikipedia.org/wiki/G-force#Horizontal_axis_g-force)
15g = 15 times the force of gravity on Earth which is 9.8 m/s = 147m/s
30,000,000/147 = 204081 seconds = 3401 minutes = 56 hours