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We derived a relation for Mach’s principle by applying Schwarzschild’s procedure to solve Einstein’s equations within a homogeneous mass sphere. This results in the proportionality relation \(c^2 \sim \frac {MG}{R} =\Phi .\) We then use this conclusion to extend the solution to a three-dimensional sphere as a model of the spatial component of space-time. For a stationary model of the universe as a three-dimensional sphere in four-dimensional space, the following possible proportionality coefficients are calculated. Two cases of the action of the law of gravity are introduced: for distances within the sphere and for distances within the four-dimensional space.

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The Schwarzschild’s Solution and Mach’s Principle

  • 会议论文

  • 发表日期：

    2025年

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  • Goce Chadzitaskos

摘要

We derived a relation for Mach’s principle by applying Schwarzschild’s procedure to solve Einstein’s equations within a homogeneous mass sphere. This results in the proportionality relation \(c^2 \sim \frac {MG}{R} =\Phi .\) We then use this conclusion to extend the solution to a three-dimensional sphere as a model of the spatial component of space-time. For a stationary model of the universe as a three-dimensional sphere in four-dimensional space, the following possible proportionality coefficients are calculated. Two cases of the action of the law of gravity are introduced: for distances within the sphere and for distances within the four-dimensional space.