Relativity and Cosmology

    

A Static, Infinite Universe: Gravitational Redshift and the Tolman Test Revisited

Authors: Marco Aurelio De Cunha

This paper revisits the application of the Tolman surface brightness test in the con-text of a static, homogeneous, and isotropic universe with a uniform mass density D.The gravitational redshift z(R, D) is derived using the exact spherical metric withoutweak-field approximations. The apparent velocity v(R, D) is calculated relativistically,leading to the derivation of the luminosity distance RL through an integral approach.The implications of this framework on the Tolman test are explored, revealing a correc-tion that accounts for gravitational curvature effects. A detailed discussion is providedon the philosophical motivations behind Einstein’s original static model and its topo-logical finiteness, which aligns with modern LCDM models. Special attention is givento the historical oversight of gravitational redshift in static universe models, which ledto misinterpretations of observational data.

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[v1] 2025-04-04 22:05:38

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