Saul said:
There is a second issue as to what is happening in the massive object at a subatomic level to create the massive magnetic field. Typically the first step is more observation evidence to guide and bound the model and mathematics. The generation of strong magnetic field in other astronomical objects might be one place to look for observation data to discuss. I am having a look and will see if I can get something to start a thread with.
Yes, and you'll find it a very rich and complex field with a huge amount of open questions. The other thing is that the same process that causes magnetic fields in neutron stars and black holes are likely to be more or less the same thing that causes the Earth's magnetic field. One thing that is curious is that we don't have a complete understanding of what causes the Earth's magnetic field, and a lot of the models which we have for magnetic fields in astrophysical objects are "toy models" which may be very, very wrong.
One thing that does come out of the research is that the processes that are involved in creating neutron star magnetic fields are very different from what causes black hole magnetic fields. Basically neutron star magnetic fields could come from movements of materials within the neutron star, whereas black hole magnetic fields come from things that are happened at the "surface" of the black hole.
Also, it's generally believed that astrophysical magnetic fields don't come from subatomic processes, but from the motion of conducting fluids. One piece of evidence for this is that most objects (including the Earth) have temperatures that are above the Curie point which means that the magnetic field doesn't actually come from the atoms themselves. Also you can show that if the Earth's magnetic field did come from the material in the earth, that it would have disappeared a long time ago.
This is something that people spend their entire careers studying. It's really cool stuff.
I think that everyone assumes because the mathematics is intimidating that the analysis assumptions are not open to criticism and do fundamentally affect the conclusions.
I don't find the math in Mitra to be intimidating. The problem is that I look at the math and start foaming at the mouth and start screaming "this is utter rubbish" people who aren't familiar with the math start looking at me like I'm acting irrationally. Basically, I'm looking at his arguments, and to me it's as if you were to see someone say "2+2=5!" and be proud of discovering "2+2=5!"
The base assumptions should be stated and approved. Mitra has specific criticisms which seem fundamental. It would be interesting to discuss and clarify Mitra's criticisms and then to see if a GR specialist would respond.
What Mitra is saying is that if you take the equations for a collapsing star and then put them into the equations for GR, then it takes an infinite time for the star to collapse. The problem is that he is using the wrong equations.
Go to equation 28 in that paper. If you are right outside the event horizon the the first part of the equation goes to zero. So if you use this as your coordinate system then the variable that you are calling "time" stops at the event horizon, and if you ask "how much time" does it take for anything to happen, the answer is the answer that Mitra gets, which is infinity. If you use equation 28 for your coordinate system then when you get close to the black hole, everything freezes, and it freezes precisely because you have chosen a coordinate system in which "time" stops at the surface of the black hole.
The problem is that you have selected the coordinate system so that this happens. It's like flying over the north pole in spherical coordinates, if you ask how fast your are moving in angular coordinates as you fly over the north pole, you get nonsense answers But even thought polar coordinates gives you silly and absurd answers of you try to use them over the north pole, it's a convenient way of locating points on a sphere.
It's the same principle here.
Now the reason I notice this is that when I write my simulations of supernova collapse, I use something like Mitra's equation 28 in my simulations. The reason I do this is that I want the simulation to be well behaved so that I intentionally choose a definition of "t" and "x" so that "t" slows down at the surface of the forming black hole. I do this because I'm not really interested in what happens inside the black hole (since I can't observe any of that), so I have the computer run the inside of the simulation at a slower and slower speed so that the inside of the simulation never actually becomes a black hole. But I intentionally define time and space this way so that I get this result. It gives me the right answers for things outside the black hole (which I care about), but it gives me misleading answers for anything near or inside the black hole (which I don't care about).
One other way of thinking about it is "bullet time". In the movie the Matrix, the film makers speed up or slow down parts of the movie for dramatic effect. Same sort of principle here. When I'm running supernova simulations, I try to have things where the "action is" happen at normal speeds where as I trying to "slow down" parts of the simulation that I'm not interested in. Since relativity says that I have some flexibility in coordinate systems, I choose a coordinate system in which this behavior happens, that what that is is equation 28.
If you look at equation 28, you'll see that the number in front of "du" goes to zero as you cross the Schwarzschild radius. What this means is that you've *intentionally* set up the coordinate system so that you never see something crossing the event horizon.
Also, I'm not a GR specialist. I know just enough GR to run computer simulations, but what I've just said I think is a pretty standard consensus view.