No apparent horizon in a Schwarzschild black hole?

An apparent horizon is the boundary between radially outwards directed photons that fall in before they reach you and those which do reach you. If you are in the frame of an external stationary observer rays on the horizon never reach you, as you can see in Droste coordinates. But if you transform to the frame of an infalling observer, the rays at the horizon do reach you when you fall through it, which can be seen in Raindrop coordinates, where the g_rr component of the metric tensor is not 0 anymore. For the transformation from Droste to Raindrop click here, but there is still a horizon - just not an apparent one. So you can still see your feet when you fall into a black hole, but the light they emitted after they crossed the horizon will only reach your eyes after your head crossed the horizon too.