On the use of the entropy principle in general relativity

The main purpose of this article is to use the extension of thermodynamics to general relativity, previously proposed by the author, to obtain expressions which will give the criteria for the thermodynamic equilibrium of a static gravitating system in a readily applicable mathematical form. After restating the principle chosen by the author as the general relativity analogue of the second law of thermodynamics, and showing once more that it is a natural covariant generalization of the ordinary second law of thermodynamics, the principle is then applied to finite systems in general and to adiabatic systems having no flux of matter or heat at the boundary. The mathematical conditions for thermodynamic equilibrium are then obtained for the case of any finite static system, and a specially useful form for these conditions is obtained for the case that the system has spherical symmetry