Canonical ensemble for rotating relativistic systems

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.