[lutusp]

> Are the trajectories of light beams following the curvature of space-time reversible? In other words, if I reflect a light beam back on itself, does it return to its source?

Yes, it would, assuming you have a way to reflect a beam back the way it came, like the kind of retro-reflectors the Apollo astronauts left on the moon. If you were an observer and saw a laser beam emanating from some distant place, and you wanted to assure that your laser beam would be most likely to be seen there, you would point it at the exact opposite heading -- assuming neither the source nor destination were in motion.

> Because if that's true (and my feeble understanding is that it is true), then light can't enter a black hole or the reverse path would allow light to escape.

That's a different question with a different answer. If you point a laser beam at a surface that absorbs most or all the radiation that falls on it, it's possible that none of the initial radiation will be returned to the source. But -- very important -- all the energy is accounted for. If the initial light beam has energy E, then the energy absorbed and reflected by the target will also equal E, not necessarily the same wavelengths but the same total energy. This applies to black holes as well -- they conserve energy.