Authors: Steven Kenneth Kauffmann
The calculations of Oppenheimer and Snyder showed that quasi-Newtonian cycloidal metric and energy density singularities in the behavior of an initially stationary uniform dust ball in "comoving" coordinates fail to carry over to "standard" coordinates, where that contracting dust ball at no finite time attains a radius (quite) as small as its Schwarzschild radius. This physical behavior disparity reflects the singular nature of the "comoving" to "standard" transformation, whose cause is that "comoving time" requires the clocks of an infinite number of different observers, making that "time" inherently physically unobservable. Notwithstanding the warning implicit in the Oppenheimer-Snyder example, checking other "comoving" dust ball results by transforming them to physically reliable coordinates is seldom emulated. We here consider the analytically simplest case of a dust ball whose energy density always decreases; its "comoving" result has a well known singularity at a sufficiently early time. But after transformation to "standard" coordinates, that singularity no longer occurs at any finite time, nor is this expanding dust ball at any finite time (quite) as small as its Schwarzschild radius. But this dust ball's expansion rate peaks at a substantial fraction of the speed of light when its radius equals a few times the Schwarzchild value, and the "standard" time when this inflationary expansion peak occurs is roughly equal to the "comoving" time of the "occurrence" of the unphysical "comoving" singularity.
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