Authors: Steven Kenneth Kauffmann
The "collapse" of a solely gravitationally-interacting, energy-conserving dynamical system necessarily involves the time evolution of a bound state of that system. An archetypal feature of energy-conserving bound state time evolution is its cyclicity, its predilection to forever revisit the parts of phase space it has previously touched. Thus it isn't surprising that the energy-conserving position-independent dust density gravitational model of Oppenheimer and Snyder produces a Robertson-Walker metric that is time-periodic, specifically time-cycloidal. In fact a mere pair of Newtonian point masses, starting from relative rest at nonzero separation, also executes a specifically time-cycloidal degenerate gravitational trajectory. Relativistic upgrade of that model causes the two particles to respect a minimum mutual separation and thus a speed limit of 0.866c, subtly changing shape details of the basic Newtonian cycloid in time. But no credible evidence is found that energy-conserving "gravitational collapse" can be other than cyclic in character: Oppenheimer and Snyder erroneously disrupted their time-cycloidal Robertson-Walker metric by forgetting that dust of position-independent energy density is necessarily present in all of space, which leaves no physical scope for their "application" of the Birkhoff theorem. Oppenheimer-Snyder dust of position-independent energy density is furthermore highly unphysical: its infinite dust energy causes the Oppenheimer-Snyder metric to violate the Principle of Equivalence. So for spatially localized dust only numerical computations are inherently credible.
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