Can one make inferences about what is inside a Black Hole?

[Craine]

Consider if you will…
…a large black hole, with an event horizon 1 light year in diameter. If an observer shoots an electron into the event horizon on one side, how long does it take for an observer on the opposite site of the black hole to register the increased electric charge and mass?

Normally I’d say it would take 1 year.

However, in that case it means that the black hole’s electric field and the shape of the event horizon are uneven during that time. It would mean that observers can make inferences about matter that has entered the black hole in the past by making careful observations of the shape of the event horizon, the electric field and the rotation.

Is that possible? Or is the black hole a true singularity, and is the charge transmitted to the opposite site immediately? (spooky action at a distance).

 

[Stingray]

No changes in the electric field are ever going to travel faster than light. It should be said, however, that the meaning of this statement is much more subtle than in flat spacetime: light may take multiple paths between two events, and some field components may propagate faster than some of the light beams taking more circuitous paths.

It also isn't particularly clear when to say that the black hole has "absorbed" the charge. Electric fields near black holes behave a little differently from what you'd probably expect. If you take a small charge and hold it just outside the horizon of a spherically-symmetric black hole, the electric field will actually appear centered on the hole rather than the charge (unless you go very close to it).

For these and other reasons, there is no straightforward answer to your question except to say that there's nothing spooky going on.

 

[bcrowell]

First off, there's no real need to talk about charge here. The issues are all the same if you just talk about gravity, with no E&M. If you drop an electrically neutral object into a black hole, what will happen is that the object will radiate gravitational waves on its way in. These gravitational waves will be refracted around the black hole, and they will also be Doppler shifted toward lower frequencies as they radiate up out of the gravity well. As the object approaches the event horizon, the Doppler shift as observed at infinity approaches infinity, and the waves become undetectable. Theoretically the gravitational waves start radiating at the instant when you release the object. If the observer is on the other side of the black hole, and the circumference of the event horizon is 2pi light years, then it will take at least pi years for the first waves to reach the observer, starting from the time of release.

Or is the black hole a true singularity, and is the charge transmitted to the opposite site immediately? (spooky action at a distance).

No. The phrase "spooky action at a distance" refers to quantum entanglement, and this is a classical problem. Even in quantum mechanics, quantum entanglement doesn't propagate information at >c.

Note that the no-hair theorems in GR are theorems about static solutions. This isn't a static solution.

 

[bcrowell]

It also isn't particularly clear when to say that the black hole has "absorbed" the charge. Electric fields near black holes behave a little differently from what you'd probably expect.

I think the right way to think about it is that as the charge approaches the event horizon, the EM radiation Doppler shifts infinitely, and the EM fields detected by a distant observer asymptotically approach the field you'd expect from a charged black hole.

If you take a small charge and hold it just outside the horizon of a spherically-symmetric black hole, the electric field will actually appear centered on the hole rather than the charge (unless you go very close to it).

Really? This sounds wrong to me, but I'm prepared to be convinced by evidence to the contrary.

 

[Craine]

Okay, I actually agree.

But that also seems to indicate that by carefully measuring the shape of the event horizon, gravitational waves and all, an observer can make inferences about matter that has fallen into the black hole in the past. Inferences about matter now inside the event horizon.

I was under the impression that this is not supposed to be possible?

 

[Stingray]

I think the right way to think about it is that as the charge approaches the event horizon, the EM radiation Doppler shifts infinitely, and the EM fields detected by a distant observer asymptotically approach the field you'd expect from a charged black hole.

I agree, but there's no distinct time where you'd look at the radiation and say "the charge was absorbed now."

Really? This sounds wrong to me, but I'm prepared to be convinced by evidence to the contrary.

The original article appears to be http://link.aip.org/link/JMAPAQ/v12/i9/p1845/s1" , but the result probably isn't too obvious from their equations. To quote,

In this paper we consider the problem of a point
charge slowly lowered into a Schwarzschild black
hole as a simple example where the final outcome
can be investigated. We find that, as the charge is
brought near the horizon, the electrostatic field
remains well behaved, while all the multipole
moments, except the monopole, fade away, so that
a Reissner-Nordstrom black hole IS produced.

You can also see p. 50 of the membrane paradigm book: http://books.google.com/books?id=T9...e paradigm electric field black hole&f=false". The horizon acts a little like a conducting membrane.

 

[Stingray]

Okay, I actually agree.

But that also seems to indicate that by carefully measuring the shape of the event horizon, gravitational waves and all, an observer can make inferences about matter that has fallen into the black hole in the past. Inferences about matter now inside the event horizon.

I was under the impression that this is not supposed to be possible?

Nothing inside the horizon can propagate out, but we're only talking about radiation originating from things outside of the horizon. From an external perspective, things don't ever quite fall through the horizon anyway. And in practice, the evidence of things falling in that we're talking about decays very quickly (but not completely).