Nah, he's a crackpot at par with Shubert.
You're new here so perhaps you don't know but he's a postdoc in mathematics somewhere, clearly those people whose job is it to know good research think he's capable of it.
That might be but:
-he doesn't understand the underlying physics, this became clear when he maintained that a change of notation changes the equations from being non-covariant to becoming covariant
Where did he say that? He talked about changing from an equation which wasn't covariant to one which is. When he said $$\eta \to g$$ he didn't mean change notation he meant when you construct, from the ground up, a formalism where you don't assume the metric is the Minkowski one then you obtain a result which is of the same form as the flat space version but instead of partial derivatives you have covariant ones, which include connection terms. $$\partial \to \nabla$$ isn't a change of notation, its an entire change of formalism to say "I no longer ignore connections", which is what you do if you only use partial derivatives. Yes, when you then say "Having formalised this for the general case I now consider the special case of the Minkowski metric" then $$\nabla = \partial$$ but this is because $$\nabla = \partial + \Gamma$$ with $$\Gamma = 0$$ if $$g = \eta$$. He clearly
wasn't talking about a change of notation but a change of formalism.
$$\partial^{a}F_{ab}$$ is only covariant if you view $$\partial$$ as $$\nabla$$ with the connection manifestly set to zero by the metric choice. Saying $$\partial \to \nabla$$ is not a change of notation from that respect, few people competent at relativity would view it in such a way.
-he has no proof that the tensor transformation rules apply to implicit functions other than his unsubstantiated claims'
The tensor structure invariance under general coordinate transformations do not require you to have an explicit analytic expression for the transformation, an implicit one still defines some transformation and provided you can use the implicit demonstration to demonstrate a non-singular Jacobian then the coordinate transformation is valid. J is defined by some $$\tilde{x}^{\mu} = \tilde{x}^{\mu}(x^{\nu})$$ and how that dependency is expressed is irrelevant provided the definition of $$\tilde{x}^{\mu}$$ allows you to demonstrate a valid Jacobian.
Alpha says that you are an expert, why are you so reluctant to do a simple calculation to prove it to yourself?
I don't think I used the word 'expert', I said he's likely better than many, if not all, of the PhDs here in certain things and while that's no small thing that doesn't automatically equate to 'expert'. Being a postgrad or postdoc doesn't make one a genius, as plenty of said postgrads and postdocs will readily admit.
And Guest's abilities can be discerned without having to see him do simple algebra, he's able to hold his own in discussions, as are any of the other regular posters here who say they have formal education beyond degree level.
