INTRODUCTION OF ISOTROPIC BLACKBODY RADIATION INTO THE INHOMOGENEOUS COSMOLOGICAL MODELS OF SZEKERES

The analysis carried out by Szekeres on the inhomogeneous space. time ds2 = dt2 exp (2a) dr2 exp (23)(dy2 + dz2), where a and &#x03D0 are functions to be determined, with an irrotational dust source, is repeated when the energy-momentum tensor includes a term due to isotropic thermal radiation as well. The method is found to work still, provided that the function &#x03D0 does not depend upon r, but is only tractable analytically when the Gaussian curvature of the two-metric exp (2v)(dy2 + dz2) vanishes, v representing the spatial part of ß. The universe described by this cosmological model possesses two important properties: first, the limiting form of the equation of state of all the matter present, as we return to the origin of the Universe, is p=e, characterizing stiff matter; and secondly, the Universe can never become anisotropic or inhomogeneous in the future. (All perturbational and gas dynamical effects are ignored.) © Royal Astronomical Society.