Thermodynamics induced geometry of self-gravitating systems

Abstract

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.