Can a Magnetic Field Escape a Black Hole?

[cragar]

If light can't escape a black , Then can a magnetic field escape a black hole ,
If the B field has an energy density , and if it has energy associated with it then it should be affected by gravity .

 

[cragar]

come on someone has to have some input on this , Any input will be much appreciated .
Let me phrase the question another way , if I have a strong bar magnet and it has a
B field associated with it and this bar magnet is getting pulled into the black hole and it crosses the event horizon , does the B field of the magnet exist past the event horizon or does the black hole bend the B field of the magnet .

 

[ansgar]

the B field lines will be infected by the gravitational field lines i.e. the curvature in space time.

so what do you think will happen?

 

[cragar]

I think the B field will get pulled in by the black hole , That might sound crazy .

 

[tom.stoer]

The B field existed outside the BH - and its "relict" will stay to exist outside. When the magnet is pulled inside the BH, it crosses the EH exactly with the speed of light - as measured by an observed sitting at the horizon - so it leaves behind an electromagnetic wave outside the BH.

In order to calculate this process magnetostatics is certainly not sufficient. One has to use ful electrodynamics in curved spacetime and I bet the calculations will result in a relict-electromanetic wave.

The first guess is that the magnet itself is in free fall and therefore there should be no acceleration and no electromagnetic wave emitted fromthe magnet. But the magnet is not pointlike and that's why free fall does not apply; it will feel a huge tidal force when it crosses the horizon. This tidal forces pulls the magnet away from its B field. The free fall w/o force is applicable only in a tiny region around one point in space, not globally. Therefore there is an acceleration of one point of the magnet with respect to another point in space at which you observe the B field.

Hope my ideas are clear ...

 

[cragar]

Interesting , thanks for your response .

 

[tom.stoer]

It may sound strange that massive objects cross the horizon with the speed of light. That's possible because the horizon is not a spacelike but a timelike surface.

If you look at radially outgoing light rays emitted in the neighborhood of a black hole there are three cases:
- they are emitted outside the EH, that means they will escape to infinity
- they are emitted inside the EH, that means they will converge to the singularity
- they are emitted exactlyat the EH,that means they will stay at the EH!

The third case shows that the EH "s made of light frozen at the EH". As light moves (with respect to any massive object) at the speed of light; the obejcts cross the horizon = the "frozen light" at the speed of light. The coordinate system where the observer is at rest at the horizon is not a physically system; no real observer (except a frozen photon) can exist at the horizon.

 

[cragar]

It may sound strange that massive objects cross the horizon with the speed of light. That's possible because the horizon is not a spacelike but a timelike surface.

So when the magnet has crossed the event horizon , and let's say it emits a photon in the direction of travel will the photon appear to be at rest from the magnets perspective.


And just to be clear a magnetic field can escape a black hole is this correct.
And what if a photon was emitted from the field from the inside of the black hole towards the EH , and it was emitted directly opposite of the acceleration of gravity , Would the photon be gravitationally red-shifted to zero or what would happen .

 

[tom.stoer]

So when the magnet has crossed the event horizon , and let's say it emits a photon in the direction of travel will the photon appear to be at rest from the magnets perspective.

No, with respect to the magnet the photon still travels with the speed of light.

I only wanted to make clear why the magnet crosses the horizon with the speed of light. Perhaps it's better to explain it the other way round: the horizon is moving with the speed of light because it's a litgh-like surface.

And what if a photon was emitted from the field from the inside of the black hole towards the EH , and it was emitted directly opposite of the acceleration of gravity , Would the photon be gravitationally red-shifted to zero or what would happen .

No, it will not be red-shifted to zero. It will never reach the horizon at all but fall into the singularity. It's rather strange: the magnet is falling towards the singularity. The photon is emitted towards the horizon. Nevertheless the photon leaves the magnet in the direction towards the singularity with the speed of light. Somehow the direction owards the EH ceases to exist physically.

Regarding redshift: You always need two reference frames in order to define it, one frame is the free-falling system of the magnet. But once the photon has been emitted it will never be observed at the magnet, so the definition of a reference frame to measure redshift at the magnet is somehow meaningless. All reference frames to measure redshift must be located between the magnet and the singularity. Therefore in all these frames the photon will be observed blue-shifted.

Inside the EH rather strange things happen. Somehow space becomes timelike. In normal situations you (or any other massive object) can only travel along future-directed world-lines. Inside the EH you can only move along world-lines directed towards the singularity.

That is basically the modern definition of an event horizon in terms of trapped surfaces. Think about an arbitrary spacelike surface with two normals. Regardless in which direction (along which normal) light rays are emitted they will eventually converge towards the singularity. Somehow one could say that no other directions exist. That's comparable to the situation at the north pole of the earth: there is no other possibility than to move towards the south pole. Other directions simply do not exist.