I have been working on what I thought would be a (reasonably) simple problem and I have found it to be completely intractable.

The concept is simple enough...I wanted to let a rocket fall into a black hole while applying a constant acceleration of its own. But after problem after problem (I can't tell you how many curvature tensor components I've been cranking out) I can't seem to get a grip on it.

So, what I am asking for is some help. The problem I am looking at is that I am going to specify $\displaystyle \frac{dx}{d \tau} = a$ with no other gravitational sources being considered. How can I derive a possible metric satisfying this condition? Conceptually I see no major problem with this but I just can't manage to do it. It's driving me bonkers!

Thanks!

-Dan