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Thermodynamic equilibrium in relativistic rotating systems

The thermodynamic equilibrium configurations of relativistic rotating stars are studied using the maximum entropy principle. It is shown that the heuristic arguments of Thorne (1971) and Zeldovich (1969) for the equilibrium conditions can be developed into a maximum entropy principle in which the variations are carried out in a fixed background spacetime. This maximum principle with the fixed background assumption is technically simpler than, but has to be justified by, a maximum entropy principle without the assumption. Such a maximum entropy principle is also formulated in this paper, showing that the general relativistic system can be treated on the same footing as other long-range force systems.