eFTC-260301

General Solution of the Central Symmetric Problem
20 March 2026

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Abstract

We present the general solution of the central symmetric problem. Our treatment applies to both the interior and exterior regions of a spherically symmetric astrophysical extended matter source with finite radius. It applies as well to the case of singular matter sources. Explicit calculations are provided for the cases of the so-called standard metric as well as the Combridge-Janne family of metrics. The latter is recognized as the exterior solution, not a vacuum solution, of a configuration with singular matter sources lying anywhere between the origin and the Schwarzschild radius. The particular case of the true Schwarzschild metric remains the only one with a consistent physical interpretation since it remains regular for the entire range of the radial coordinate, the origin of which is hosting the singular matter source.

Copyright © 2026 Yvan Leblanc. All rights reserved

PACS: 4.60.+n, 11.17.+y, 97.60.Lf

Cite as: Leblanc, Y., "General Solution of the Central Symmetric Problem", Report no. eFTC-260301 (2026). http://www.efieldtheory.com/abs/?eFTC-260301; doi:10.13140/RG.2.2.18801.34407.