# Bob and Alice at the Event Horizon again.

1. Apr 12, 2013

### Staff: Mentor

You may be weary of the repeated questions about event horizons. The concepts are slippery.

Imagine Bob and Alice. Bob free falls into the black hole. For simplicity, assume he falls along a radial geodesic with no tangential component. Alice remains outside to observe.

Alice observes Bob getting smeared over the surface and getting red shifted out of existance.

Bob observes nothing remarkable at all (as long as he remains far from the singularity). That's where I have trouble understanding.

Suppose Bob extends his arm pointing at the center of the black hole. At some point Bob's hand is inside the event horizon but his eyes are not. Won't his hand disappear?

Even inside it seems that his hand should remain disappeared. Suppose the Schwarzschild radius is R1, Bob's eye is at R2, and Bob's hand at R3. R3<R2<R1. The curvature of space at R1 is just enough to guarantee that no interior geodesics crosses the R1 boundary, but at any smaller radius R the curvature is even more.

Then light leaving Bob's hand at R3 finds no geodesic extending radially outward to Bob's eye at R2. Of course as Bob moves inward, his eye eventually arrives at R3 and could meet some photons emitted from his hand earlier, but the image of the hand would be totally smeared.

According to this logic, in the interior volume of the black hole, no light or information should be able to travel radially outward regardless of the starting point. In effect, all interior radii are event horizons.

Even looking backward toward the horizon, I think Bob should see the distortions caused by gravitational lensing. Light from stars at the periphery of Bob's vision should appear to shift closer to the radial center of his gaze.

So I reason that Bob sees nothing but a black smear looking radially inward, and nothing but a point source of light looking radially outward. How can it be that Bob observes nothing remarkable at all?

2. Apr 12, 2013

### Passionflower

Nope, because by the time light from his hand reaches his eyes his eyes also have passed the event horizon, so therefore he can always sees his hand.

Why do you think the image would be smeared?

Now an interesting thought experiment would be:

Imagine a free falling (from infinity) extended object of length L falling through the event horizon. At what point, if at all, does the distance between the front and the back of L increase faster than c?