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I have read this question:

Charged particle is accompanied with EM radiation (has field that falls with distance as 1/r) when it moves with acceleration.

Does a constantly accelerating charged particle emit EM radiation or not?

It emits light, because it "stirs up" the electromagnetic field. To understand this, just dip your finger into a still pond and move it in a circle. Water waves will emanate from your finger. These waves have energy, which means energy is being taken away from you. Same goes for the charges. In fact, this follows almost automatically from the finite propagation speed of light. The electric field of a stationary charge obeys Coulomb's law. If the charge suddenly starts moving, the field won't obey Coulomb's law anymore, but it can't instantly change everywhere because of the finite propagation speed. Instead a "shockwave" of information goes out from the charge at speed c. This shockwave contains electromagnetic energy and travels at the speed of light -- it is light.

enter image description here

Why does an accelerated charge radiate away energy?

So based on these, two things come to mind:

  1. all accelerating charges emit EM radiation (because they stir up the field)

  2. nothing can escape a black hole (neither should the EM radiation)

And I cannot reconcile these two at the same time, because if light (EM radiation) cannot escape the black hole, then how does it emit it if it is accelerating?

Question:

  1. Does an accelerating charged black hole emit EM radiation?
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  • $\begingroup$ Can two charged black holes interact? Will their courses change? If you vibrate a hole will it emit radiation? Seems so. Like when you vibrate an electron. $\endgroup$
    – MatterGauge
    Feb 14, 2022 at 23:33
  • $\begingroup$ Could two charged black holes circle one another because of charge? $\endgroup$
    – MatterGauge
    Feb 15, 2022 at 0:18
  • $\begingroup$ Off course they emit energy. How are they accelerated? In an electric field. $\endgroup$
    – MatterGauge
    Feb 15, 2022 at 0:22
  • $\begingroup$ Many of your black hole questions have the same answer - there is nothing inside a real black hole. Everything that ever falls in remains at the horizon forever, including the original matter of the collapsed star. $\endgroup$
    – safesphere
    Feb 15, 2022 at 15:51
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    $\begingroup$ Also note that it is not trivial to accelerate a black hole. You cannot simply push or pull it like in your picture. You need either strong tidal gravitational forces or a strong electromagnetic interaction. $\endgroup$
    – safesphere
    Feb 15, 2022 at 16:30

2 Answers 2

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Yes, it will radiate. The light does not come from inside the black hole. The accelerated charge of the black hole affects the electromagnetic field around but outside the event horizon.

You could ask the same question you are asking now about gravitational waves. Binary black hole systems radiate gravitational waves, even though a gravitational wave that fell into a black hole could not escape.

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  • $\begingroup$ But don't the EM waves propagate from the space immediately surrounding the charge, ie in the blackholes event horizon. And thus cannot escape? Isn't the reason that gravitational waves can propagate outwards is because it is the fabric of spacetime itself waving, instead of something IN that fabric? Can you give me a link to a source? $\endgroup$
    – jensen paull
    Feb 15, 2022 at 0:16
  • $\begingroup$ Also if your correct. Then wouldn't blackholes lose energy, WITHOUT hawking radiation.... $\endgroup$
    – jensen paull
    Feb 15, 2022 at 0:17
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    $\begingroup$ @jensenpaull I am not sure if anyone has actually done this calculation or not. But it's pretty clear that you will have radiation. A charged black hole will act as a source term for the electromagnetic stress-energy tensor in the Einstein-Maxwell equations. There's no problem with conservation of energy, because an accelerating black hole needs an input of energy from somewhere; that is also the source of the radiated energy. (A stationary charged black hole wouldn't radiate). $\endgroup$
    – Andrew
    Feb 15, 2022 at 0:22
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    $\begingroup$ @jensen From math.ucr.edu/home/baez/physics/Relativity/BlackHoles/… In this sense the black hole is a kind of "frozen star": the gravitational field is a fossil field. The same is true of the electromagnetic field that a black hole may possess. $\endgroup$
    – PM 2Ring
    Feb 15, 2022 at 0:28
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    $\begingroup$ @jensenpaull Light isn't escaping the black hole. There's some EM field surrounding the black hole when it is stationary. Then you accelerate the black hole. The EM field near the horizon will follow the horizon. The EM field a little further away from the horizon will obey Maxwell's equations. Maxwell's equations tell the field at a given point in space how to change, given what the field looks like in a neighborhood around that point. It doesn't matter if the field lines are connected to a point charge or a black hole. The field lines are changing. This will lead to a wave solution. $\endgroup$
    – Andrew
    Feb 15, 2022 at 0:45
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You need to take into consideration how the hole is accelerated. That's because other charges create a field. And just as two electrons, interacting by virtual photons, can create a real photon not coming out of themselves, a hole can do this to. And as @Andrew says, two holes can emit real gravitational waves (real gravitons), not coming out of the hole. The internal of the hole doesn’t change. Only the surrounding condensate of photons (or gravitons).

Brehmstralung

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