Is the Stephani-Krasiński solution a viable model of the Universe? |
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| Authors: | D Lorenz-Petzold |
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| Institution: | 1. Fakult?t für Physik, Universit?t K.onstanz, D-7750, K.onstanz, FRG
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| Abstract: | We present a detailed study of the inhomogeneous Stephani-Krasinski solution with time-dependent curvature index. In general,
the cosmological behaviour of the models depends on six arbitrary functions of time. Such models are termed ‘private universes’
and cannot be in accord with observation in the most general case. Two simple models with changing topology are considered
as illustrating examples. In one of these models the pressure turns out to be negative and hence a violation of the weak energy
condition in the singularity theorems is possible. A brief review of other inhomogeneous cosmologies is included for the sake
of clarity. It is shown that the geodesic equation can be reduced to a complicated differential equation, which depends on
the three arbitrary functions involved. Therefore, it is difficult to obtain explicit formulas for the various observational
relations. |
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| Keywords: | cosmology inhomogeneous — general relativity |
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