Authors: Steven Kenneth Kauffmann
In 1922 Alexandre Friedmann obtained, in the context of an unusual spherically-symmetric metric form, formal solutions of the Einstein equation for dust of uniform energy density which as well apply within spherically symmetric dynamic dust balls of uniform energy density. The resulting Friedmann equation for the dynamical behavior of these ostensibly general-relativistic dust-ball solutions exclusively reflects, however, completely non-relativistic Newtonian gravitational dynamics, with no trace at all of the purely relativistic phenomenon of gravitational time dilation, notwithstanding that gravitational time dilation inescapably accompanies gravitation's presence in GR. That paradox wasn't noticed by Friedmann, nor has it since been consciously addressed. As a consequence, accepted dust-ball behavior is Newtonian gravitational in every respect, notably including compulsory deceleration of dust-ball expansion, as well as compulsory assumption by every expanding dust ball of a singular, zero-radius "Big Bang" configuration at a finite earlier time -- despite both behaviors being incompatible with the implications of gravitational time dilation. The source of these inconsistencies is the GR-incompatible nature of Friedmann's unusual metric form, which extinguishes relativistic gravitational and speed time dilation by implicitly utilizing the GR-inaccessible set of clock readings of an infinite number of different observers. However in 1939 Oppenheimer and Snyder carried out a tour-de-force analytic space-time transformation of a Friedmann GR-unphysical dust-ball solution which satisfies a particular initial condition to fully GR-physical "standard" metric form. That Oppenheimer-Snyder transformation was recently extended to arbitrary dust-ball initial conditions, yielding the equation of motion in fully GR-physical "standard" coordinates of any dust ball's radius. This non-Newtonian GR-physical dust-ball radius equation of motion fully conforms to the implications of gravitational time dilation: it in no way forbids acceleration of dust-ball expansion, but it prevents, at any finite "standard" time whatsoever, any dust ball's radius from being smaller than or equal to its Schwarzschild radius-value. Full GR conformity thus needs no "dark energy", but can't support a "Big Bang".
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