Cosmological Schwarzschild radii and Newtonian gravitational theory

Physics

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Educational Aids, Relativity And Gravitation, Spacetime Topology, Causal Structure, Spinor Structure

Scientific paper

We describe Friedmann-Robertson-Walker zero-pressure dust-filled universes using a Schwarzschild-like curvature spatial coordinate R along with the usual cosmological time coordinate t. In terms of coordinates (R,t), the geodesic equations of general relativity for the motion of the galaxies comprising the universe satisfy exactly a Newtonian inverse-square relationship. This allows us to formulate relativistic cosmology by starting first with Newtonian cosmology. After the mathematics of Newtonian cosmology is worked out, the general-relativistic metric for the universe is constructed from a well-defined prescription, and the behavior of light signals is then determined from the metric. It is found that certain radial light signals born at the Big Bang eventually reach a maximum distance in their journey through the universe, where they turn around and return to some arbitrarily chosen origin. The turning around takes place at an apparent horizon located at a Schwarzschild radius in the universe.

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