Authors: Steven Kenneth Kauffmann
The self-gravitational correction to a localized spherically symmetric static energy distribution is obtained from an upgraded Newtonian model which is energetically self-consistent, and is also obtained from the Birkhoff-theorem extension of the unique "Newtonian" form of the free-space Schwarzschild metric into the interior region of its self-gravitationally corrected source. The two approaches yield identical results, which include a strict prohibition on the gravitational redshift factor ever being other than finite, real and positive. Consequently, the self-gravitationally corrected energy within a sphere of radius r is bounded by r times the "Planck force", namely the fourth power of c divided by G. That energy bound rules out any physical singularity at the Schwarzschild radius, and it also cuts off the mass deviation of any interacting quantum virtual particle at the Planck mass. Because quantum uncertainty makes the minimum energy of a quantum field infinite, such a field's self-gravitationally corrected energy essentially attains the Planck force times that field's boundary radius r. Roughly estimating r as c times the age of the universe yields a "dark energy" density of 1.7 joules per cubic kilometer. But if r is put to the Planck length appropriate to the birth of the universe, that energy density changes to the enormous Planck unit value, which could quite conceivably drive primordial "inflation". The density of "dark energy" decreases as the universe expands, but more slowly than the density of ordinary matter decreases.
Comments: 9 pages. Also archived as arXiv:1212.0426v2.
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