Witness the Sky of an Accelerated Black Hole

[jartsa]

Let's put an observer hovering near the event horizon of a charged black hole.

As the black hole is charged we can change its velocity from zero to 10 m/s in one second.

But we can not send a message to the observer in one second.

So the observer does not know that the black hole that he is sitting on started moving. So I guess he is moving with the black hole.

Why does he not see stars moving? I mean those stars that were still in the black hole's sky when the black hole was not moving, why do those stars stay still when the black hole and the observer start moving?

 

[SlowThinker]

As the black hole is charged we can change its velocity from zero to 10 m/s in one second.

You are ignoring that the electric field only moves with the speed of light.

But we can not send a message to the observer in one second.

And yet it takes a long time for the light to reach the observer.
These 2 premises cannot be true at the same time.

 

[jartsa]

You are ignoring that the electric field only moves with the speed of light.

Hey that's one more oddity: The observer can't measure any electric field although the electric field is already accelerating his black hole.

We know that a charged black hole attracts opposite charges when charges come nearby, right? Therefore charges attract oppositely charged black hole when they come close together. Attraction is mutual.

 

[DaveC426913]

But we can not send a message to the observer in one second.

Sorry, where are we when we are sending this message?

So the observer does not know that the black hole that he is sitting on started moving.

He'll know when it starts moving under him.

So I guess he is moving with the black hole.

Why?

Why does he not see stars moving? I mean those stars that were still in the black hole's sky when the black hole was not moving, why do those stars stay still when the black hole and the observer start moving?

What?

Perhaps others can grasp what you're describing, but I need a clearer picture.
Can you re-describe your scenario from the top including the middle steps?

 

[jartsa]

Perhaps others can grasp what you're describing, but I need a clearer picture.
Can you re-describe your scenario from the top including the middle steps?

Because of gravitational time dilation a message takes a long time to reach a person in a gravity well.

As a black hole moves in gravity fields like any other object, I assume that a charged black hole moves in electric fields like any other charged particle.

When we attract the black hole with charges, while observing the person near the event horizon, we see that the black hole and the person start moving, but only after a long time we see that the person has noticed that he has started moving, the information that somebody is messing with the black hole reaches him after the black hole has been moving a long time.

 

[PeterDonis]

As the black hole is charged we can change its velocity from zero to 10 m/s in one second.

One second relative to whom? There is no absolute time. I suggest that you give a more detailed description of what is happening.

I guess he is moving with the black hole.

Don't guess. Calculate.

 

[SlowThinker]

I'll ask a related question, that might answer the original question.
When we move a charged ball at some reasonable distance from the BH (not very close to the horizon), when does the horizon move?
Does the EM wave have to reach the singularity first, and the horizon follows, or is the horizon itself moved by the field?
Or does the horizon behave in such a way that the distinction is nonsensical?

 

[PeterDonis]

When we move a charged ball at some reasonable distance from the BH (not very close to the horizon), when does the horizon move?

The horizon is not a "place", so you can't really think of it as "moving" when the charge distribution changes but "standing still" otherwise. It's a null surface, generated by outgoing light rays.

Also, the known solution that describes a charged black hole assumes that there is no other charge or stress-energy present anywhere. If you put another charge in, you are changing the solution; we don't have a known solution that describes this case. So we don't know for sure how the horizon would behave.

Finally, when we are dealing with relativistic solutions, we have to keep in mind the fact that charge and stress-energy can't just appear from nowhere or disappear into nowhere. You can't have a solution where you suddenly place a charge that wasn't there before, or turn on an EM field that comes out of nowhere, with no pre-existing energy or charge anywhere. The solution has to obey all conservation laws everywhere, otherwise you get nonsensical answers. That is why I asked jartsa to give a more detailed description of what is happening.