Quote by juanrga
It is evident that this kind or argument can be inverted. People as Hawking, experienced in black holes and general relativity, can say nonsense when entering in the field of thermodynamics.

Exactly. That's why argument to authority fails. In this situation, I think Hawking is right.
Even if we ignore now that «the energy that is in the gravity field» is not welldefined in general relativity, what you say about thermodynamic energy and gravitation seems to be without any basis.

It's pretty simple. Gravitational potential energy makes up a substantial amount of energy in astrophysical objects. Hence arguments based on energy conservation that ignore interactions of the gravity field just don't work. If you introduce the gravity field, the situation that Hawking finds is pretty standard.
Already many ordinary textbooks explain how gravitational energy [itex]M\phi[/itex] contributes to thermodynamic energy. Of course, in a BH the situation is more complex and [itex]M\phi[/itex] is not enough, but thermodynamics in presence of gravitation continues to hold and I fail to see your point.

My point is that adding gravitation introduces additional terms into the energy equation, and once you introduce those terms, the arguments in the paper break down. The paper makes arguments that ignores the impact of gravity on the thermodynamic equations, and you just can't do that.
Gravity changes everything. Once you have a gravitational field, then adding or removing energy from the system will cause interactions with the gravitational field, and *that's* what gives you heat capacities that you don't see in nonself gravitating objects.
Black holes are not monoatomic ideal gasses. Because of selfgravitation, black holes are different enough so that you can't even use monoatomic ideal gasses as an analogy.