Thought experiment for using Black Holes for cmmunication

[NateTG]

Let's say that we have two planets -- planet A and planet B, 100 Lightyears apart in space. Centered directly between them is a black hole with a 25 lightyear Schwartzchild radius. (The idea is that it's 25 lightyears fromt the Schwartzschild surface to each planet.)

If someone on planet A shots a stream of electrons with velocity .99c into the black hole, then awouldn't someone on planet B be able to observe the change in the black hole in approximately 50 years by observing the charge of the black hole?

The electrons would take about 25 years to reach the black hole. Then the black hole would have observable charge. Since the internal structure of the black hole is unobservable, the charge should affect all of the black hole instananeously, so the other side would also be changed. Then the observation of the charge chage would take another 25 years to reach the other planet.

I see two potential answers:
One is that the black hole has an effective diameter of zero -- thus the distnace between the planets is actually 50 lightyears.
The other is that the charge propogates along the schwartzchild surface of the black hole at c, so that it takes less time for light to get from one planet to the other by barely missing the Schwartzschild horizon.

 

[MathematicalPhysicist]

Originally posted by NateTG
Let's say that we have two planets -- planet A and planet B, 100 Lightyears apart in space. Centered directly between them is a black hole with a 25 lightyear Schwartzchild radius. (The idea is that it's 25 lightyears fromt the Schwartzschild surface to each planet.)

If someone on planet A shots a stream of electrons with velocity .99c into the black hole, then awouldn't someone on planet B be able to observe the change in the black hole in approximately 50 years by observing the charge of the black hole?

The electrons would take about 25 years to reach the black hole. Then the black hole would have observable charge. Since the internal structure of the black hole is unobservable, the charge should affect all of the black hole instananeously, so the other side would also be changed. Then the observation of the charge chage would take another 25 years to reach the other planet.

I see two potential answers:
One is that the black hole has an effective diameter of zero -- thus the distnace between the planets is actually 50 lightyears.
The other is that the charge propogates along the schwartzchild surface of the black hole at c, so that it takes less time for light to get from one planet to the other by barely missing the Schwartzschild horizon.

if we assume that the speed of electron is constant even when it's already inside the black hole and the escape velocity from the black hole is c therefore i think the electron should pass the whole 100 lightyears distance between the stars and therefore it will take it to come to planet be 100 years and not 50 because i don't think a black hole is a shortcut.

 

[marcus]

Originally posted by NateTG
... Since the internal structure of the black hole is unobservable, the charge should affect all of the black hole instananeously...

For me, your thought experiment points out the need to examine
that "fact" about black holes having no hair
or the idea that a black hole is completely characterized by three
parameters: mass, spin, and charge

I suppose that this can be true only for a BH in isolation, not interacting with environment (gaining charge, mass, angular momentum)
If the BH is in the middle of some dynamic interaction with the outside world then the event horizon can be undulating and the EM field around the hole can be changing too.

the info that the hole has acquired some charge (a steadily increasing amount if it is a steady beam of electrons) would
travel by maxwell equations I guess, anyway not instantaneously.

this is not to say that I can solve the problem presented by this thought experiment----I am merely telling you what I learn from the experiement: that a BH in the midst of some interaction (like a planetsize chunk of matter has just fallen into it, or a bag of charge, or whatever, and it is digesting the thing and maybe burping) cannot be simply described by just three numbers.

it must have more than 3 degrees of freedom IMHO

maybe someone else can give a more authoritative account