I launch my shuttle from the mothership on a straight-line course tangent the a blackhole’s event horizon at a contstant velocity. I understand the crew will see my ship as steadily decelerating since it will take an infinite amount of time (from their point of view) for me to reach my goal).
What will I see, both looking forward to the event horizon and backwards at my ship? Is there a point where the gravitational lens will bend light enough that I will see multiple images of the mothership?
There exist null geodesics (photon trajectories) wrapping arbitrarily many times around a black hole before re-escaping toward infinity. This means that however far away you are from a black hole, there exist paths that light can take from you, around the black hole one or more times, and back to you (or back to another point). Practically speaking, these images are faint and distorted (very squashed in the radial direction), so it will be difficult to detect these multiple images. Looking forward toward the event horizon, you will see black (or Hawking radiation, if you’re looking closely). As you approach more closely, the horizon covers more and more of the visible sky.
Here’s a nice set of images which show rays from a faraway background of stars, past a black hole, to a Schwarzschild-stationary observer at various distances from the horizon. A note of caution, repeating the one at the bottom of that page: These images are for stationary observers. An infalling observer will see something different.
Actually, Hawking radiation doesn’t exist for a free-falling observer.
Good point. I can’t tell from his description whether his spaceship is freefalling or not, though.