Does GR provide a limit to the maximum electric field?
I've gotten conflicting information regarding this, and am quite confused. I will try to quote exactly when possible so as not to confuse things more with my paraphrasing.
The author of the Motion Mountain physics textbook claims in his book there is a limit, and clarifies on his site that ( http://www.motionmountain.net/wiki/index.php?title=Dislike_Page ):
"electromagnetic fields are limited in magnitude. Now, every electromagnetic field contains energy, and energy density is limited by general relativity: if energy density is too high, a black hole appears. The smallest possible black hole then leads to a field limit. If you deny an upper field limit, you deny general relativity. However, general relativity has been confirmed in every experiment so far."
This sounds very obvious and intuitive to me. However one of my physics TA's got very upset when I used this in a thought experiment when discussing some limits in physics. When I told him the textbook I got that from, he looked it up, and commented on the Motion Mountain wiki website his argument:
"I'd like to add something here. Suppose for a moment the energy density limit is correct, then if an object is sped up until it length contracts enough such that the energy density is greater than this limit, does it turn into a black hole? No, quoting John Baez "The answer is that a black hole does not form"* http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html *The claim that "if energy density is too high, a black hole appears" is an incorrect oversimplification. The issue is that in GR, gravity depends on more than just the energy density (component T^00 of the stress energy tensor). So we can't just look at the "relativistic mass" (E/c^2) to judge whether a black hole forms. It actually isn't even enough to look at the "invariant mass", for while the trace T of the stress energy tensor for a particle is just its invariant mass, for an electromagnetic field it is identically zero even though electromagnetic fields curve spacetime in GR. So none of these concepts of mass are sufficient when discussing gravity using GR (especially when considering electromagnetic fields), because gravity couples to the entire stress energy tensor. I hope this was helpful."
This makes much less sense to me, and I don't understand how energy density tending to infinity could EVER avoid being a black hole. No offense to my TA, but I'm skeptical as he's disagreeing with a textbook author. Plus, the author's response was that my TA is another Einstein denier, and not worth responding to.
So I'd like a third party's answer on this. Does GR provide a theoretical limit to the strength of an electric field? Is it best to just ignore my TA on this one?