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Should a black hole, in the absence of all external electromagnetic forces, generate its own magnetic field? Would all particles in the vicinity of the black hole by effected by this magnetic field--i.e., are there any particles that do not respond to some magnetic force?

Joshuah Heath
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Max
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    What does the second part of your question have to do with black holes? A magnetic field exerts no force on a particle with no charge (e.g. a neutrino). – ProfRob Jun 11 '17 at 07:07
  • Related: https://physics.stackexchange.com/q/39161/2451 and links therein. – Qmechanic Jun 11 '17 at 10:34

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A non-rotating black hole can have an electric field, but the difference between electric and magnetic fields depends on the restframe. An electric field in motion generates a magnetic field and vice-versa. Hence, black holes can be said to have magnetic fields, in particular if they rotate. Electric and magnetic fields always come together.

You may instead ask why a black hole has electric charge but no magnetic charge. That's because in Maxwell's theory of electrodynamics, there are no magnetic monopoles. If there were magnetic monolopes, black holes could also have magnetic charge. (These things are known as 'dyonic black holes'.)

As to why the electromagnetic field of a black hole has the form it has, that's simply what you get if you solve the Maxwell-equations coupled to General Relativity.

WIMP
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The definition of a black hole describes a body that's information is hidden behind an event horizon if the black hole has a magnetic field the field must be limited to within the event horizon as otherwise the field could have a causal effect on events outside the horizon and violate the definition

8Mad0Manc8
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    I think you should read a bit about the Reissner-Nordström black holes. In essence, yes the BH can have electric field out of the EH. – peterh Jun 11 '17 at 01:14
  • Surely without reading the advised info the event horizon separates an external observer from any event that occurs within it . knowledge of those events would predispose the nature and logic of an horizon it's simply we do not know the nature of events it may seem like an intellectual Dodge like a lot of answers but an event horizon is simply another way of saying we cannot describe with any certainty and our knowledge extends beyond the boundary and events external to it. – 8Mad0Manc8 Jun 11 '17 at 01:28
  • The event horizon prevents information from inside the event horizon from reaching the universe outside the event horizon. So the gravitational field and electromagnetic field that the collapsing star has as it collapses into a black hole gets essentially frozen into a "fossil" field. See this old Usenet FAQ article How does the gravity get out of a black hole? There are also relevant pages here on SE.Physics. – PM 2Ring Jun 11 '17 at 01:34
  • @PM2Ring without reading the link does the description of fossil field include the limitations of its spacial influence to be within the event horizon and can it only effect the contents within the horizon as in my reasoning or is a black holes event horizon more loosely defined. – 8Mad0Manc8 Jun 11 '17 at 14:57
  • The key point is that no information can cross from inside the EH (event horizon) to outside the EH, so whatever happens inside the EH cannot change anything outside it. And that means that the gravitational and electromagnetic fields outside the EH become stuck in the state they were at when the matter that originally caused them fell inside the EH. – PM 2Ring Jun 11 '17 at 15:33
  • (cont) However, this is just a description in terms of pure GR, it doesn't take quantum mechanics into account, so it ignores Hawking radiation. OTOH, for black holes of stellar mass and greater, the amount of energy emitted as Hawking radiation is miniscule: Hawking radiation for such BHs is calculated in the microkelvins or even nanokelvins, so it's currently swamped by the 2.725 kelvin temperature of the CMBR. – PM 2Ring Jun 11 '17 at 15:33
  • @PM 2Ring so are you saying that any electromagnetic fields observed at the boundary of the event horizon eminating into space surrounding it originated from the matter entering the event horizon and cannot be causally effected by the fate of the matter from whence they originated because of the event horizon causal boundary the fields remain in a unchanging state and there not as a result of the state of the matter within the event horizon and have therefore no link with the black hole – 8Mad0Manc8 Jun 11 '17 at 15:45
  • @PM2 Ring are u saying the calculated hawking radiation eminating from the black hike a concept I don't understand because again it contradicts the definition and meaning of an event horizon. However despite that the hawking radiation is therefore undetectable because of the cosmic background microwave radiation. – 8Mad0Manc8 Jun 11 '17 at 15:55
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    Yes, that's exactly what I'm saying. In pure general relativity the EH is a causal boundary so the fields outside the EH are no longer affected by the matter / energy inside the EH. Quantum mechanics modifies this picture slightly. Roughly speaking, the Heisenberg uncertainty principle means that the position of the EH is not exact, instead it's slightly "fuzzy". – PM 2Ring Jun 11 '17 at 16:04
  • @PM2 Ring I've read in other questions that in order to understand the physics involved within the event horizon we need to have an explanation of quantum gravity once we do then effectively remove the event horizon boundary because we would be able to explain the events within it but isn't there a kind of paradox there in order to have an explanation of quantum gravity would we have to observe events within it and take this information out of the black hole in order for us to formulate an explanation or will we be able to formulate an explanation simply out of our imagination? – 8Mad0Manc8 Jun 11 '17 at 16:18
  • A theory of quantum gravity (hopefully!) will allow us to create a mathematically & physically consistent description of what happens to matter / energy when it reaches the centre of a black hole, in general. The EH will still be an information boundary, so we won't be able to verify the QG theory of the core of a BH by direct observation. But that's ok: it's unlikely that we'll ever be able to verify our theories of what happens in the core of a normal star by direct observation either. ;) – PM 2Ring Jun 11 '17 at 16:32