Canonical ensemble for rotating relativistic systems

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Abstract
The Euclidean action formalism of Gibbons and Hawking (1977) has been developed explicitly to take into account the finite size of relativistic rotating systems. It is shown that for a general stationary axisymmetric metric the entropy turns out to be a sum of contributions from matter and black hole automatically. The suggested approach generalizes the one York and co-workers (1986) developed for a spherical symmetrical gravitational field.