Exact Bianchi IV cosmological model

Mathematics

Scientific paper

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Astronomical Models, Big Bang Cosmology, Einstein Equations, Field Theory (Physics), Asymptotic Methods, Gravitational Waves, Metric Space, Relativity, Singularity (Mathematics), Tensor Analysis

Scientific paper

A solution to the Einstein field equations is obtained in closed form for the simplest choice of a metric for a Bianchi IV cosmological model. For the most part, Cartan symbolic methods are used to obtain components of the Ricci tensor. The solution is shown to be axisymmetric, to have a true singularity in the finite past, and to be asymptotically flat as time tends to infinity. It is found that the model cannot be persistently diagonal in either the vacuum or perfect-fluid situation, that the simplest nondiagonal case will possess a solution only if the cosmological constant is zero and no matter (i.e., perfect fluid) is present, and that an electromagnetic field is admissible as a source only in the lowest mode. It is noted that the evolution of this model is the same as that of 'big bang' models except for the remarkable feature that it is devoid of matter.

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