To clarify the analogy in my previous post. I don't mean that QFT is like GR, nor that SM is like LCDM. I mean that SM relates to QFT like LCDM relates to GR.
I'd refer to the following analogy.
QFT is like GR when SM is like LCDM.
GR can fit many different cosmological models, and the open questions are about actual contents and history of the universe, which are the aspects I refer to as being "in addition" to the GR framework.
QFT is a framework that fits models with massive as well as massless neutrinos, with one as well as five generations of particles, with photons as well as phonons, with vacuum as well as solid state, etc. I mean that all the missing questions are specific to the model, i.e., SM, and are in addition to QFT.
Schwarzschild metric and all related derivations such as photon sphere, are valid in vacuum. If we start adding a significant amount of energy there, we need to consider a different metric and different effects.
I remember that charged particles moving in rotating magnetic fields are involved in the description of this, but it was too long ago (and not in my main line of study) to recall details. Hope to see some expert answers.
Philosophy is certainly neither pseudoscience nor science. It is also not football, chess, music, engineering, cooking, etc. I think that "love of wisdom" is a good definition.
Well, the instantaneous change of acceleration, in the case of circular motion, happens to be also "along the direction of motion, perpendicular to the instantaneous acceleration". However, I don't know how they (i.e., the time derivative of acceleration and the radiation) are related and don't claim anything in this regard. My point in this post was that AFAIK, a constant acceleration of charged particle can be insufficient to cause radiation.
Something is missing in this definition. As it is described, the simple solution would be just to have a "result" some constant or, more generally, independent on the variable "a".
AFAIK, not every acceleration causes radiation from a charged particle. For example, in synchrotron radiation the acceleration is perpendicular to the particle velocity. In some other cases, a magnitude of acceleration is variable. Is it correct?
If the light orbiting the BH is not a test particle but rather has the energy as described in the OP, then I think it is not on a photon sphere anymore. The "photon sphere" of the original black hole would be inside the new black hole.
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