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Revisiting the Anisotropy of the Schwarzschild Metric

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This version is not peer-reviewed

Submitted:

24 October 2024

Posted:

25 October 2024

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Abstract
The Schwarzschild metric encompasses both exterior and interior regions, with a reversal of signature upon transition from one to the other when using Schwarzschild coordinates. In the interior region, the radial spacelike coordinate transforms into a timelike radius, introducing a time-dependent scale factor on the interior metric's angular term. Though the interior metric is a Kantowski-Sachs type metric, by examining the geometry in Kruskal-Szekeres coordinates, we find that the interior geometry must be spatially isotropic and homogeneous. The azimuthal term of the metric is describing the 'spin' of a reference frame relative to the surrounding shell and it is this spin that goes to infinity at the singularity, not the density of the 2-sphere. After detailed analyses supporting these hypotheses, we investigate why the interior Schwarzschild and FRW metrics, which are both spatially homogeneous and isotropic metrics, treat space and time so differently.
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Subject: Physical Sciences  -   Astronomy and Astrophysics
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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