Can the Magnetic Field of a Black Hole Reveal Its Charge and Rotation?

[Dr Lots-o'watts]

By observing the magnetic field of a black hole, couldn't a charge density depending on radius, as well as a rotational speed, be determined? I presume a charge(radius) function can be determined, so that would mean there was mass following a circular trajectories, somewhere between the singularity and the event horizon. Is that right? Is that allowed? What am I missing if not?

 

[nismaratwork]

By observing the magnetic field of a black hole, couldn't a charge density depending on radius, as well as a rotational speed, be determined? I presume a charge(radius) function can be determined, so that would mean there was mass following a circular trajectories, somewhere between the singularity and the event horizon. Is that right? Is that allowed? What am I missing if not?

Within the event horizon, I don't believe that concept applies... if you're asking whether or not a BH can have a charge or external magnetic field, then yes it can. Polar jets are (probably) the result of the magnetic field generated by the accretion disk and ergoregion.

 

[zhermes]

By observing the magnetic field of a black hole, couldn't a charge density depending on radius, as well as a rotational speed, be determined? I presume a charge(radius) function can be determined, so that would mean there was mass following a circular trajectories, somewhere between the singularity and the event horizon. Is that right? Is that allowed? What am I missing if not?

The answer is completely undefined and unknown. According to general relativity the singularity has NO physical extent. Also keep in mind the quantum nature of things like 'spin' (e.g. of an electron). Its not associated with an actual rotation/orbit. Just because these ideas apply in casual low gravity, normal scales cases; doesn't mean they apply for black-holes.

 

[Nabeshin]

The existence of electric or magnetic fields for black holes is usually attributed to the particles "freezing in time" as they fall towards the event horizon with respect to an outside (at infinity) observer, thus freezing the field lines with them. I've always found that description a bit unsettling, but its the best explanation I've ever heard (since clearly anything inside the EH cannot communicate with the outside world).

 

[nismaratwork]

The existence of electric or magnetic fields for black holes is usually attributed to the particles "freezing in time" as they fall towards the event horizon with respect to an outside (at infinity) observer, thus freezing the field lines with them. I've always found that description a bit unsettling, but its the best explanation I've ever heard (since clearly anything inside the EH cannot communicate with the outside world).

What isn't unsettling about a BH near the EH?

 

[Dr Lots-o'watts]

The answer is completely undefined and unknown. According to general relativity the singularity has NO physical extent. Also keep in mind the quantum nature of things like 'spin' (e.g. of an electron). Its not associated with an actual rotation/orbit. Just because these ideas apply in casual low gravity, normal scales cases; doesn't mean they apply for black-holes.

Yet couldn't there be mass in "perpetual orbit" (in the same sense as any other orbit), somewhere between the singularity and event horizon? Seems that it would be a very special case if this space was empty.

 

[Nabeshin]

Yet couldn't there be mass in "perpetual orbit" (in the same sense as any other orbit), somewhere between the singularity and event horizon? Seems that it would be a very special case if this space was empty.

No. There are no stable orbits any closer than r=6GM/c^2 away from the singularity, and the innermost unstable circular orbit occurs at r=3GM/c^2.

Or if you're interested in a less analytical answer, the simple fact is all light cones inside the event horizon are directed completely inward. So it would be impossible to orbit as you are forced to move inwards (the analogy is that space and time switch roles inside the EH. That is, while you are obligated to move forward in time outside the EH, you are similarly obligated to move inward in radius while inside the EH).

 

[twofish-quant]

By observing the magnetic field of a black hole, couldn't a charge density depending on radius, as well as a rotational speed, be determined?

It turns out that black holes like most astrophysical objects can generate large magnetic fields without being charged. Kip Throne worked out the math and if you imagine the black hole as if it were a conducting sphere, you end up with a model that you can use to do calculations of the magnetic field.

 

[Dmitry67]

It turns out that black holes like most astrophysical objects can generate large magnetic fields without being charged. Kip Throne worked out the math and if you imagine the black hole as if it were a conducting sphere, you end up with a model that you can use to do calculations of the magnetic field.

But I guess it violates no-hair theorem, isn't it?

 

[twofish-quant]

But I guess it violates no-hair theorem, isn't it?

Turns out no. What is happening is that the magnetic field is attached to things that are just outside of the event horizon.

 

[rhyshanan]

the matter falling in them might be.