I expect people to make equations for the masses of quantum and cosmological black holes and the relationship between these masses, can these possible equations be necessary and sufficient to introduce quantum gravity?
The definition you mention for quantum gravity is not absolute. Nobody today has an ultimate definition of what quantum gravity is, it all depends on the theory you are referring to. I am absolutely certain that there is a very close relation, in terms of calculation, between the masses of quantum black holes and the masses of cosmological black holes. Which means that there is a very close link between a quantum Schwarzschild radius and a cosmological Schwarzschild radius what I say should not bother anyone, however one must be open to theories that may seem exotic that is experimentation which should proves the one or the other theory! The problem isn't whether I'm following or I'm not following the same theory you're following – the problem is much more fundamental. For me the units of Planck, general relativity, and special relativity are unifieded by the cosmological constants it is on this subject that I work to make an ultimate theory capable of calculating the universe from its infinitely small to its infinitely large and believe me I get incredible results. Unitile to work outside of these three theories that I just mentioned Einstein and Max Planck gave people all the means to unify physics just keep thinking within the framework of their works without adding almost anything except to discover the cosmological constants that are missing, but there people must have super creative ideas to continue the work of these distinguished physicists!
The topics I covered on RG are very well chosen, meticulously prepared and targeted. My questions will soon be followed by articles containing lots of equations in all the subjects of physics within the framework of a unified physics based as I always say on general relativity, special relativity, and the Planck units supported by cosmological constants. All this to give people new perspectives to better understand things that are still fuzzy in physics.