A point-particle model universe

Mathematics

Scientific paper

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Astronomical Models, Cosmology, Gravitation Theory, Relativistic Theory, Space-Time Functions, Field Theory (Physics), Points (Mathematics), Singularity (Mathematics), Tensors

Scientific paper

A description is presented of a model in which the observable cosmos is modeled as a set of point-particles, representing the galaxies, which perturb a dust-filled, Robertson-Walker space-time. In the development of the model, use is made of a metric considered by McVittie (1965). Attention is given to notation and fundamental definitions, the model, the potential equation, the nature of the singularities, and the extension to many particles. The field equations employed are those of Einstein with a cosmological constant. The equations define an energy tensor T in relation to a metric g. g assumes the form considered by McVittie (1965). Both necessary and sufficient conditions are established for this equation to give rise to an energy tensor of a specified form.

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