In darkest night

"Nothing can escape the event horizon of a black hole." This is a given in physics. In particular, it is impossible to transmit information from the inside of the event horizon to the outside.

But the event horizon is, presumably, mappable from without; you can look at it in 3-space and measure its boundaries. And it, presumably, is centered on the singularity within it. If the singularity moves, the event horizon moves with it.

Why is it not possible to enter the event horizon, either in a heavy spaceship or with another singularity in your pocket or something, and transmit information out by moving the two masses relative to each other? If you fly a heavy mass from one side of singularity A to the other, the event horizon's boundaries will move, yes? People outside would see them move, yes? It would be like two golf balls beneath a blanket—they might look like a single lump, but if one of them were rolling around the other the lump would appear to move. And thus you would have a (rather unwieldy, but theoretically possible) telegraph from the inside of the event horizon.

I am missing something here. What is it?

This weekend

What should I do in Montréal this weekend?

Calcutta

(No, the song is not a cover of the Buffy song. Alas.)

Restating my black hole conundrum in a more intuitive way:

Say we send a robot (of arbitrarily large mass) to orbit a distant star. With a plumb-bob of sufficient sensitivity (and no other masses in the universe), we could track our robot's orbit: assuming we're in the plane of the ecliptic, the plumb-bob would oscillate back and forth, pointing at the center of mass of the robot/sun system as the robot orbited from one side of the star to the other. If the robot moved into a lower/faster orbit, the plumb-bob's amplitude would drop, and its frequency would increase.

Replace the star with a black hole; nothing changes. The robot drops into lower and lower orbits, and each time it does we watch our plumb-bob's behavior change. Finally, the robot drops inside the event horizon...and you would think the robot could continue to affect our plumb-bob: signaling to us by dropping into lower orbits in a prearranged pattern, for instance. But it can't, since information cannot leave a black hole.

Phrased like this, the answer seems clear: we never see the robot reach the event horizon, because time slows down near a black hole, and appears to stop at the event horizon. From our plumb-bob's point of view, the center of mass is no longer moving; the robot is stuck like a fly on the event horizon, and never will move again. (Beep.)

But we talk about "rotating" black holes—if time stops at the event horizon, how is it possible to detect a black hole's rotation? What does it even mean to have a "rotating" black hole, if everything within the event horizon is frozen, as far as the outside world is concerned? Hmmm.