So, as with the many fictitious characters that have preceded me, I am going to drop into a black hole - and I will bring along Alice, that "outside observer" who hangs around black holes waiting for "Bob"s to drop in.
I am going to take along a gravitational altimeter. And I'm going to use a gravitational altimeter design that I believe is easier to model in the BH environment. That altimeter will just be side-by-side pendulums of equal length. At the top they will be a fixed distance...