This is a reasonable restatement, but it doesn't change the main point of what I said, the the energy in question is not usefully viewed as "kinetic" energy.

But how do you arrived at that conclusion? Because it does not seem reasonable to me. Say you have five excited electrons in potential well. So all of them have some energy. One of them can fall to lowest energy level and give up it's energy. This energy should be considered as "kinetic energy". But other four electrons can't fall to lowest energy level any more so they should have some of their energy considered as 'kinetic energy" and some as other type of energy just because they were not the ones that have fallen to lowest energy level. And if no electron falls to lowest energy level? How do we split between "kinetic energy" and the other energy? This does not make sense to me.

You can't. That's my point. None of the energy you are talking about is usefully thought of as "kinetic" energy, because it has nothing to do with the temperature of the electrons--they can all be at absolute zero and it would still be true that only one (or two if we consider their spin) can occupy the lowest energy level. So whatever it is that is keeping the other electrons from occupying the lowest energy level, it has nothing to do with "motion" of the electrons (they're all at absolute zero) and nothing to do with "kinetic" anything (the temperature is absolute zero).

But zero temperature being equivalent to zero kinetic energy works only in classical physics and not when you bring QM into the picture. In QM even at zero temperature particles have non-zero momentum.

The existence of an objected projected by theory is more properly an experimental or observational question, so I am somewhat befuddled and disappointed by the discussion's focus on the theory rather than by observational evidence.

A better way to frame the key questions from the viewpoint of encouraging skepticism and examination of the evidence is:

What evidence is there to support the existence of black holes?

and

What are the alternative explanations of the available evidence?

Well, the question as given by OP is not about existence of extremely massive and compact objects out there. The question is about current theoretical model of these extremely massive and compact objects.

The question should be slightly different. How we can test that these massive objects we observe out there are adequately represented by our theoretical models.
And there we come to the problem that current theoretical model does not allow direct confirmation but only indirect (interior of model BH is out of our causal future).

Finding weak spots or less reasonable assumptions in mainstream model should point in what direction to look for alternative models.
When we have alternative model we can work out predictions that could tell apart alternative model from mainstream model by observation.

The article in your second link reports the findings of this paper: https://arxiv.org/abs/1503.03873
Basically research takes slightly different path. It examines what alternatives can be discarded based on observational data we can gather. Such approach is better than nothing but it leaves verification of the theory vulnerable to confirmation bias IMO.

So I don't see that examining the theory is waste of time.

This is post from BTSM that I didn't get an answer to:

I admit i know little about this subject, but am interested in any thing that solves the singularity problem.
May be some one will look at this paper to see if it makes sense

arXiv:1709.09794 (cross-list from gr-qc) [pdf, other]
Falsifying cosmological models based on a non-linear electrodynamics Ali Övgün, Genly Leon (Catolica del Norte U.), Juan Magaña, Kimet Jusufi
Comments: 36 pages, 14 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th)

Recently, the nonlinear electrodynamics (NED) has been gaining attention to generate primordial magnetic fields in the Universe and also to resolve singularity problems. Moreover, recent works have shown the crucial role of the NED on the inflation. This paper provides a new approach based on a new model of NED as a source of gravitation to remove the cosmic singularity at the big bang and explain the cosmic acceleration during the inflation era without initial singularity on the background of stochastic magnetic field. We explore whether a NED field can be the origin of the cosmic acceleration. Also, we found a realization of a cyclic Universe, free of initial singularity, due the model for the NED energy density we propose. We find explicit relations for H(z) by direct integration of the equations of motion of the proposed model. We perform MCMC likelihood exploration of these relations using Observational Hubble data to find the mean values for the NED parameters. We compute the deceleration parameter q(z) in the range 0<z<2 from the best fit values of the parameters and find q(z)→1/2 at z→∞. Moreover, the Universe passes of a decelerated phase to an accelerated stage at redshift ∼0.5. The result is that the are not statistical differences with the usual model during the radiation epoch which holds for α=0. However, taking α slightly different from zero, we find that the NED with dust matter (wm=0) is able to drive the late-time cosmic acceleration of the standard cosmological model.

No, in QM at zero temperature particles still have nonzero energy (because "zero temperature" means "ground state", and the energy of a particle in the ground state is still nonzero). If the particles are in a potential well, the ground state is most likely going to have zero expectation value of momentum (for example, consider the 1s state of the hydrogen atom) by rotational symmetry.

Energy of particle consists of potential energy plus kinetic energy. But as I understand this there is no certain split between these two energies. So it would mean that kinetic energy does not have specific value. Hmm, then defining pressure using kinetic energy might not work very well.

Average momentum should be zero but it does not seem that this helps with the question.

It seems that my line of argument reached some uncharted territory for me. So I will probably stop there and give it some time to seep in.

No, in a general spacetime "potential energy" can't even be defined. It can only be defined in stationary spacetimes.

I didn't say "average" momentum. I said the expectation value of momentum. A single electron in the 1s state in a hydrogen atom is not in a momentum eigenstate, so it has no definite value of momentum; but the expectation value of the momentum operator for this state is zero. "Average" momentum, OTOH, is meaningless, since there's only one electron so there's nothing to take the average of.