I Explore How Dropping Objects Into a Black Hole Changes It

[DrStupid]

Mentors' note: This thread has been split off from https://www.physicsforums.com/threads/can-you-even-fall-into-a-black-hole.992212/ because it's a different interesting question that deserves it's own thread

If there were a physics lab at the BH at the center of the Milky Way, say it was 1 LY distant from the EH of that black hole, or if some other distance makes the question more sensible, whatever distance that is, and a beacon is fired at the event horizon at 0.5 c relative to the physics lab, how much time would the clock on the physics lab measure before the beacon was observed to cross the EH?

If you assume that the black hole is a purely classical black hole, like a Schwarzschild or Kerr black hole, then the answer is infinite time.

That applies to a static black hole. But if something falls in it isn't static anymore. Is the answer still infinite in this case?

 

[Nugatory]

That applies to a static black hole. But if something falls in it isn't static anymore. Is the answer still infinite in this case?

Generally if you drop an object into a static Schwarzschild black hole, after a short period of complicated dynamic behavior it will settle down into a slightly more massive Schwarzschild black hole.

 

[DrStupid]

Generally if you drop an object into a static Schwarzschild black hole, after a short period of complicated dynamic behavior it will settle down into a slightly more massive Schwarzschild black hole.

The question is: Would an external observe see the object freezing at the new event horizon or disappearing during the short period of complicated dynamic behavior? If the object gets closer to the original EH than its own Schwarzschild radius before the EH expands to its final size I would expect it to disappear. As the final approach to the EH is exponentially this would happen quite fast. In case of a BH with the mass of the Sun it would be less than a millisecond for the last km.

 

[PeterDonis]

Would an external observe see the object freezing at the new event horizon or disappearing during the short period of complicated dynamic behavior?

Freezing at the new event horizon. The event horizon is not a locally observable surface; its location depends on the entire future history of the hole and its exterior. So the event horizon, heuristically, already "knows" that the object is going to fall in before the object reaches it, and moves outward in response so that when the object reaches the new horizon radius, the horizon is already there.

If the object gets closer to the original EH than its own Schwarzschild radius

This is not possible; the EH moves outward in advance, as above.

 

[DaveC426913]

So the event horizon, heuristically, already "knows" that the object is going to fall in before the object reaches it, and moves outward in response

Getting my head around this:

The EH is an abstract boundary wherein photons (and everything else) cannot escape). 7

As a massive object falls in, there is a volume above the (otherwise spherical) EH but below the infalling massive object from which photons have no path back to flat space. Thus, technically, that volume is now inside the EH, which is no longer spherical.

So, the EH is being reshaped (moved outward) to include that volume in flux by the spacetime curvature of the infalling mass.

Yes?

 

[Vanadium 50]

So the event horizon, heuristically, already "knows" that the object is going to fall in before the object reaches it

In the sense that a thermos "knows" to keep hot things hot and cold things cold.

 

[PeterDonis]

The EH is an abstract boundary wherein photons (and everything else) cannot escape).

Cannot escape to infinity (more precisely, future null infinity). But there is no way to know that locally. You have to know the entire 4-d spacetime geometry--in other words, the entire future of the hole and its exterior.

As a massive object falls in, there is a volume above the (otherwise spherical) EH but below the infalling massive object from which photons have no path back to flat space. Thus, technically, that volume is now inside the EH, which is no longer spherical.

As you can see, it's very difficult to describe what's going on in local language without tying yourself in knots.

This is basically correct if we interpret the on its face contradictory statements about the EH (that there is a volume "above the EH" which is also "inside the EH") appropriately (that there is a volume at a radial coordinate larger than that of the original radial coordinate of the EH which is nevertheless inside the EH).

the EH is being reshaped (moved outward) to include that volume in flux by the spacetime curvature of the infalling mass.

The "reshaping" of the EH is not a causal process. The EH starts to move outward before any information about the infalling object could have reached it by any causal process. That's why you can't really think of the EH locally. You have to think of it as a boundary that we draw after the fact, once we know the future history of the hole, to mark off the region of spacetime that, taking the entire future history into account, cannot send light signals to future null infinity.