The Oppenheimer-Snyder (OS) solution of the Einstein equations for a homogeneous dust star at a parabolic velocity (k = 0), as well as the solution for elliptic velocity (k = + 1), obtained by O. Klein and S. Weinberg by two other methods, describe the collapse in the Schwarzschild coordinates r, t. In the paper a complete solution of the dust star collapse is given by these three methods for all three velocities preserving the homogeneity – parabolic, elliptic and hyperbolic (k = 0, ± 1). The plots of worldlines, visualizing the internal structure of the star on the hypersurfaces of simultaneity t=const., are presented. They show that for large but finite t, when the surface freezes asymptotically over the star’s gravitational radius, each inner layer also freezes near its asymptote, corresponding to the effective gravitational radius for a given layer. As a result, the collapse of the star leads to the formation of the frozar, a frozen star with a completely frozen internal structure. In the late stages of collapse, when local velocities are close to the light velocity, differences in initial velocities are insignificant and all solutions tend to be parabolic. Therefore, after freezing, the observed effects are similar to those which was studied in the first paper.
|QUANTUM AND GRAVITATIONAL PHYSICS|
1-007, 23 p, 12.07.2020; doi:10.9751/QGPH.1-007.7133
|ISSN 2181-0486; EISSN 2181-0508|
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