Relativity and Cosmology

    

Is "Dark Energy" Just an Effect of Gravitational Time Dilation?

Authors: Steven Kenneth Kauffmann

When an expanding uniform-density dust ball's radius doesn't sufficiently exceed the Schwarzschild value, its expansion rate will actually be increasing because the dominant gravitational time dilation effect diminishes as the dust ball expands. But such acceleration of expansion is absent in "comoving coordinates" because the "comoving" fixing of the 00 component of the metric tensor to unity extinguishes gravitational time dilation, as is evidenced in the "comoving" FLRW dust-ball model by the Newtonian form of its Friedmann equation of motion. Therefore we extend to all dust-ball initial conditions the singular Oppenheimer-Snyder transformation from "comoving" to "standard" coordinates which they carried out for a particular initial condition. In "standard" coordinates relativistic time dilation is manifest in the equations of motion of the dynamical radii of all of the dust ball's interior shells; the acceleration of expansion of the surface shell peaks when its radius is only fractionally larger than the dust ball's Schwarzschild radius. Even so, for a range of initial conditions a dust ball's expansion continues accelerating at all "standard" times, although that acceleration asymptotically decreases toward zero. Attempts to account for the observed acceleration of the expansion of the universe by fitting a nonzero "dark energy" cosmological constant thus seem to be quite unnecessary.

Comments: 13 Pages.

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Submission history

[v1] 2016-05-18 18:12:13
[v2] 2016-05-21 10:16:13 (removed)
[v3] 2016-05-21 14:38:06 (removed)
[v4] 2016-05-24 01:53:26 (removed)
[v5] 2016-05-29 03:19:32 (removed)
[v6] 2016-05-30 08:26:49 (removed)
[v7] 2016-06-06 06:45:58 (removed)
[v8] 2016-06-07 06:06:38 (removed)
[v9] 2016-06-10 06:41:54 (removed)
[vA] 2016-06-11 09:06:51 (removed)
[vB] 2016-07-28 23:33:27 (removed)
[vC] 2016-07-29 13:19:10 (removed)
[vD] 2016-08-01 10:55:26 (removed)
[vE] 2016-08-17 18:16:27 (removed)
[vF] 2016-08-22 20:45:09 (removed)
[vG] 2016-08-31 19:26:46 (removed)
[vH] 2016-09-04 13:42:20 (removed)
[vI] 2016-10-17 15:38:02 (removed)
[vJ] 2016-11-24 05:08:21

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