|In your discussion of event horizons, you stated that light falls just like everything else. I thought that light does not speed up when falling but just gains energy—that it is blue-shifted. Conversely, when it rises in a gravitational field, it does not slow down but just loses energy—that it is red-shifted. Is that correct? — B
Yes. For very fundamental reasons, light can't change its speed in vacuum; it always travels at the so-called "speed of light." So light that is traveling straight downward toward a celestial object doesn't speed up; only its frequency and energy increase. But light that is traveling horizontally past a celestial object will bend in flight, just as a satellite will bend in flight as it passes the celestial object. This trajectory bending is a consequence of free fall. While the falling of light as it passes through a gravitational field is a little more complicated than for a normal satellite—the light's trajectory must be studied with fully relativistic equations of motion—both objects fall nonetheless.