On Inhomogeneous Cosmological Models Containing Space-Like and Time-Like Singularities Alternately

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Abstract
Inhomogeneous cosmological models in which space-like and time-like singularities occur alternately are examined. In the case that the models are vacuum or filled with a stiff fluid, it is found that the discontinuities of the energy density and curvature propagate with the light velocity from the boundary points between two different singularities and the spacetime on the null surfaces containing these discontinuities is not physically singular. If the models include ordinary fluid, the fluidal discontinuities propagate with a velocity smaller than the light velocity. In order to investigate the structure of spacetime near time-like singularities, moreover, some approximate solutions of the Einstein equations are derived on the condition that the differentiations with respect to the time variable and two spatial variables are negligible, compared with those with respect to another spatial variable.

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