On the gravitational motion of a fluid obeying an equation of state

Abstract

An exhaustive analysis of the spatially isotropic solutions of the Einstein-Maxwell equations corresponding to the shear-free motion of a perfeet fluid which obeys an equation of state relating its pressure and density is given. It is found that there are but two such solutions, the well-known Friedmann family corresponding to electrically neutral matter, and a new family of solutions corresponding to charged matter and characterized by a certain equation of state. The physical significance of the latter is shown to be limited. An analysis of the newtonian analog of the problem is also presented. It is concluded that the use of highly symmetric solutions of the gravitational field equations for the description of collapse or of other types of motion severely limits, or altogether precludes, the imposition of further conditions pertaining to the internal state of the matter. It is also concluded in connection with the cosmological principle that, if the universe is assumed isotropic and the Hubble law is used to assert that the motion of the cosmic gas of galaxies is shearfree, then the condition that the cosmic fluid obey an equation of state would imply the spatial homogeneity of the universe as well as its electrical neutrality.