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I am learning Reissner-Nordstrom black holes and I have learnt that the black hole contains a net charges. The static field due to it ( through the Energy Momentum tensor) exists even outside the event horizon. But I also know that nothing can escape out of an event horizon. So I have two questions-:

  1. Why does the electric field ( static ) of a charge on the Reissner-Nordstrom black hole exists even outside the event horizon of the black hole?

  2. If the black hole gains a some more charge ( say a charged particle does fall in the time like singularity) then the net charge on the black hole increases and a static condition is again reached. The electric field of the new static hole should also now increase. Will the change in electric field propagate outside the horizon also increase? If so how? This increase in the electric field could act as a causal influence which has now propagated outside the horizon but that should not have happened. ( The old hole had a horizon so nothing should pierce through it, and the new hole again reaches a static condition; so the change in the electric field has pierced through the horizon of the previous hole which shouldn’t have happened)

Qmechanic
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Shashaank
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1 Answers1

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The trick is, it always existed there, outside. Even before the black hole formed, it probably was a massive star, and had its static electromagnetic field (this is what you are asking about). When the black hole forms, it just happens that the event horizon (which is not a physical object, it is just a boundary) gets situated as a boundary so that the EM field exist even outside of it. No information, no particles need to travel from inside the event horizon.

As for how the electric field gets out of the horizon, the best answer is that it doesn't: it was never in the horizon to begin with! A charged black hole formed out of charged matter. Before the black hole formed, the matter that would eventually form it had its own electric field lines. Even after the material collapses to form a black hole, the field lines are still there, a relic of the material that formed the black hole.

Detection of the Electric Charge of a Black Hole

Your second question is even more trickier. What we are talking about is a static EM field. Again, the event horizon is a boundary, not a physical object. Where does the charged particle in your question come from? It comes from the outside world. When does it start to add to the strength of the static EM field of the black hole? Just when it enters the horizon? Nope. The charged particle in your question already strengthens the black hole's static EM field outside the horizon. This is the answer to your question. No need for any particle or information to travel from inside the horizon. When the charged particle enters the horizon, the static EM field of the black hole is already stronger.

Árpád Szendrei
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