Relativity and Cosmology

   

Nonuniform Dust, Oppenheimer-Snyder, and a Singular Detour to Nonsingular Physics

Authors: Steven Kenneth Kauffmann

Oppenheimer and Snyder treated in "comoving coordinates" a finite-radius ball of self-gravitationally contracting dust whose energy density is initially static; this is incisively dealt with by use of Tolman's rarely-cited closed-form "comoving" metric solutions for all spherically-symmetric nonuniform dust distributions. Unaware of Tolman's general solutions, Oppenheimer and Snyder assumed that the uniform space-filling dust solution applies without modification to the interior of their dust ball, which is validated by Tolman's solutions. We also find that all nonuniform dust solutions which adhere to the Oppenheimer-Snyder initial conditions have a time-cycloid character that strikingly parallels Newtonian particle gravitational infall, and as well renders those solutions periodically singular. The highly intricate, and thus easily misapprehended, singular transformation of the Oppenheimer-Snyder dust-ball solution from "comoving" to "standard" coordinates is re-derived in detail; it reveals the completely nonsingular nature of the dust-ball metric in "standard" coordinates. Thus the periodically-singular quasi-Newtonian character of the "comoving" dust-ball metric is an artifact of the perceptibly unphysical "synthetic" nature of "comoving coordinates", whose definition requires the clocks of an infinite number of observers.

Comments: 14 Pages.

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Submission history

[v1] 2014-08-31 23:51:55
[v2] 2014-09-03 16:57:40 (removed)
[v3] 2014-09-05 16:24:44 (removed)
[v4] 2014-09-12 03:14:18 (removed)
[v5] 2014-10-19 09:58:14 (removed)
[v6] 2015-06-11 19:31:45 (removed)
[v7] 2015-06-20 01:41:39 (removed)
[v8] 2015-06-25 01:49:53

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