Falling Feet First into a Black Hole

[Allday]

this was a kind of interesting HW problem i was working on. handed in the solution already, but don't know if it was right. ill run it by the forum and see what the members think.

what would a person see if they where falling feet first radially into a Swarzschild black hole. The person is looking at their feet the whole time. Are they always able to see their feet? (especially when their feet are inside the event horizon and their head is not). Once they cross the horizon are they still able to see their feet? Assume of course that they are not stretched apart by the tidal forces.

 

[JesseM]

This page says that you could see your feet (which is what I'd have guessed, since otherwise it seems like the equivalence principle would be violated):

One common question is whether a man falling (feet first) through an even horizon of a black hole would see his feet pass through the event horizon below him. As should be apparent from the schematics above, this kind of question is based on a misunderstanding. Everything that falls into a black hole falls in at the same local time, although spatially separated, just as everything in your city is going to enter tomorrow at the same time. We generally have no trouble seeing our feet as we pass through midnight tonight, although it is difficult one minute before midnight trying to look ahead and see your feet one minute after midnight. Of course, for a small black hole you will have to contend with tidal forces that may induce more spatial separation between your head and feet than you'd like, but for a sufficiently large black hole you should be able to maintain reasonable point-to-point co-moving distances between the various parts of your body as you cross the horizon.

If you want more of an explanation though, you'll have ask one of the GR experts on this board...

 

[Allday]

yeah that was my conclusion eventually, thanks for the link. i answered it by referencing the space time diagram with the light cones tilting in as you approach the event horizon. my reasoning was that even thought the light emitted from the feet in the radially "outward" direction is still approaching the singularity they don't do so as fast as the persons head.

gabe

 

[JesseM]

yeah that was my conclusion eventually, thanks for the link. i answered it by referencing the space time diagram with the light cones tilting in as you approach the event horizon. my reasoning was that even thought the light emitted from the feet in the radially "outward" direction is still approaching the singularity they don't do so as fast as the persons head.
gabe

Yeah, I think the tilted light cones would be the key to understanding this, that web page also emphasized them in its explanation. But what's the "they" that you're saying doesn't approach the singularity as fast as the head--the feet, or the photons? I figure once your feet cross the horizon but your eyes haven't, you can still see your feet, but you're seeing light that was emitted from your feet before they crossed the horizon. And is it also true that when you see your feet after you've crossed the horizon, you're always seeing light that was emitted from your feet when they were at a greater distance from the singularity than your eyes are currently? From the tilted light-cone diagrams, I think it must be, since the radial dimension basically becomes your time dimension once you've crossed the horizon.

 

[mijoon]

I must point out that there are very many interesting GR articles on that site as may be seen by http://www.mathpages.com/rr/rrtoc.htm" .