  A new approach based on a statistical operator is presented, which allows to
take into account the inhomogeneous particle distribution induced by
gravitational interaction. This method uses the saddle point procedure to find
the dominant contribution to the statistical sum and allows to obtain all
thermodynamic relations of self-gravitating systems. Based on thermodynamic
relations, a description of thermodynamically induced geometry of matter
distribution was proposed. Equations corresponding to the extremum of the
statistical sum completely reproduce the well-known equations of the general
theory of relativity.
