The Schwarzschild Static Cosmological Model

TL;DR

This paper introduces a 5D Schwarzschild-based cosmological model where the universe is viewed as a static, homogeneous, and isotropic star with gravitational redshift effects, offering a novel perspective on cosmology within general relativity.

Contribution

It develops a 5D immersion of the Schwarzschild solution to model the universe as a static, homogeneous, and isotropic object, integrating gravitational effects into cosmology.

Findings

Universe modeled as a static star with constant density

Redshift explained as a gravitational effect

Model obeys the square distance law and Buchdahl stability

Abstract

The present work describes an immersion in 5D of the interior Schwarzschild solution of the general relativity equations. The model theory is defined in the context of a flat 5D space time matter Minkowski model, using a Tolman like technique, which shows via Lorentz transformations that the solution is compatible with homogeneity and isotropy,thus obeying the cosmological principle. These properties permit one to consider the solution in terms of a cosmological model. In this model, the Universe may be treated as an idealized star with constant density and variable pressure, where each observer can be the center of the same. The observed redshift appears as a static gravitational effect which obeys the sufficiently verified and generally accepted square distance law. The Buchdahl stability theorem establishes a limit of distance observation with density dependence.