A REDSHIFT-MAGNITUDE RELATION FOR NONUNIFORM PRESSURE UNIVERSES

A redshift-magnitude relation for the two exact nonuniform pressure spherically symmetric Stephani universes is presented. The Kristian-Sachs method expanding the relativistic quantities in series is used, but only first-order terms in redshift z are considered. The numerical results are given both for centrally placed and non-centrally placed observers. In the former case the redshift-magnitude relation does not depend on the direction in the sky and the Friedmann limit can be easily performed. It appears that the effect of spatial dependence of pressure is similar to the effect of the deceleration parameter in Friedmann models. In the latter case the angular dependence of the relation is important. This may serve as another possible explanation of the noncompatibility of the theoretical curve of the redshift-magnitude relation with observations for large-redshift objects in the Friedmann universe. On the other hand, comparing the magnitudes of equal redshifts objects in different directions in the sky one can test the reliability of these models.