This:
Some physicists even claim that black holes will be created in particle accelerators, such as the Large Hadron Collider, potentially able to swallow the Earth.
Seconded.
--- From the paper.
An inertial frame is just somewhere Newton’s First Law holds ...
No, it's not. That's a necessary, but far from sufficient, condition. However, this error is somewhat excusable in that there are scientific sources that commit it.
General Relativity cannot violate Special Relativity by definition ...
What does that mean? It's true that GTR locally (i.e., over 'small enough' spatial and temporal regions) reduces to STR, but if the claim that STR and GTR cannot disagree, then that's trivially false.
It follows from these postulates that infinite density is forbidden because infinite energy is forbidden, ...
It doesn't follow from STR alone, the argument presented is completely ludicrous:
1. The relativistic mass diverges as v→c, and observed size tends to zero, so the relativistic mass density diverges as v→c.
2. Therefore, an object of relativistic mass density → infinity has v → c, which is impossible.
There's a very glaring difference between a conditional and its converse: A implies B is not interchangable with B implies A. A point particle (e.g., as far as we can tell, electrons are point-particles) would have infinite relativistic mass density without having infinite energy or luminal velocity.
There's also a more fundamental error of treating 'mass' and 'relativistic mass' as equivalent. It's particularly silly in this case, because relativistic mass is just an effect of viewing the same object in a different frame of reference, while a black hole remains a black hole in all frames of reference.
But we have already seen that infinite density is forbidden by the Theory of Relativity.
No, it isn't, and the argument to that effect is plainly nonsensical.
Sec.3 is mind-boggling stupid, 4 is too short to commit any major crimes against humanity, and Sec.5 contains many misunderstandings, including
--the claim that a vanishing stress-energy tensor should result in no gravitational effects, which is very curious, since there are gravitational effects in vacuum (Ricci curvature is matter, the result, Weyl curvature, is tidal forces)
--a completely spurious identification of G
μν/κ as energy-momentum of the gravitational field; this is not physics
--the claim that GTR has no conservation of energy-momentum, whereas it is in fact a mathematical consequence of the field equation, derived in almost every GTR textbook
It was early pointed out to Einstein by a number of his contemporaries that his General Theory violated the usual conservation of energy and momentum.
This is true in a sense, but far from what the author seeks to imply. Specifically, conservation of energy-momentum takes the form
--"There is no energy-momentum created or destroyed at any point in spacetime." This is analogous to the non-divergence of magnetic field lines in electromagnetism (assuming no monopoles).
but it does not allow one to say
--"The total energy-momentum is X." This is only possible in some specialized cases.
His invention was his pseudo-tensor. But Einstein (and his followers) did not realise that his invention, as well as being simply unscientific augmentation to satisfy a desire, is nonsense, for the following reason: his pseudo-tensor is in fact just a meaningless concoction of mathematical symbols and so describes nothing.
I wonder how the author feels about ordinary angular momentum in Newtonian mechanics, which, after all, is a pseudotensor of rank 1! Here's a shock: the ordinary vector cross product of two vectors is not a vector, but a pseudotensor (pseudovector, to be more precise). And guess what--cross products of vectors are not geometrical invariants either for precisely that reason.
I can deeply emphasize with the thorny issues of energy in GTR, gravitational energy in particular, but this is just pathetic. (By the way, Einstein credited for pseudotensors--??)
Sec. 6 appears to be roughly "no superposition, so we can't study it", which is silly because plenty of things are non-linear and can be studied, even computationally if all else fails (computational GTR is not a small subfield, actually). It's only notable the "there is no analytic solution, so there is no solution at all" gem of shiny pseudo-logic.
Sec. 7 sunk to new lows, and I gave up at that point.
