Here, right before your very eyes, I present you with a black hole of one solar mass which has a Schwarzschild radius of 3000 meters.
Here, also, we see a poor sad sack radially falling into the aforementioned black hole from a very great distance where spacetime was flat.
Now, the poor infalling slob notices something very strange. The Special Relativistic length contraction due to his speed exactly offsets the General Relativistic length increase between the reduced circumferences r. Ergo, his dr is the same as the reduced circumference dr.
Now, this would seen to imply that whether he travels through space, time or Jello he’s going to have to find some way to traverse that 3000 meters.
Right here, in this textbook, I see that the proper time to travel between the event horizon and the nasty place is equal to 6.57x10[sup]-6[/sup] x M/M[sub]sun[/sub] secs.
To my very great annoyance when I divide 3000m by 6.57x10[sup]-6[/sup] secs I get 4.57x10[sup]8[/sup] m/s which is not only faster than a speeding bullet, but is also faster than a speeding light. This, to put it mildly, is not good.
Now I know that the r and t change signs when the horizon is crossed, and therefore r becomes a time coordinate, but I still need enlightenment as to what is transpiring here.