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Relations between Newtonian and Relativistic Cosmology
Version 1
: Received: 26 April 2024 / Approved: 27 April 2024 / Online: 28 April 2024 (07:55:24 CEST)
How to cite: Haro, J. Relations between Newtonian and Relativistic Cosmology. Preprints 2024, 2024041823. https://doi.org/10.20944/preprints202404.1823.v1 Haro, J. Relations between Newtonian and Relativistic Cosmology. Preprints 2024, 2024041823. https://doi.org/10.20944/preprints202404.1823.v1
Abstract
The Schwarzschild metric emerges independent of Einstein's field equations, offering a straightforward derivation solely reliant on Newtonian mechanics and Minkowskian proper acceleration. This approach provides a clear path to understanding the gravitational field around a spherically symmetric mass without the need for the complexities of Einstein's full theory of General Relativity. Transitioning to our exploration of the cosmic Friedmann equations, we adopt a novel perspective rooted in a Lagrangian formulation grounded in Newtonian mechanics and the first law of thermodynamics. Our investigation operates under the assumption that the universe is populated by either a perfect fluid or a scalar field. By elucidating the intricate interplay between the Lagrangian formulation and the cosmic Friedmann equations, we uncover the fundamental principles governing the universe's dynamics within the framework of these elemental constituents. In our concluding endeavor, we embark on the task of harmonizing the classical equations—namely, the conservation, Euler, and Poisson equations—with the principles of General Relativity. This undertaking seeks to extend these foundational equations to encompass the gravitational effects delineated by General Relativity, thus providing a comprehensive framework for understanding the behavior of matter and spacetime in the cosmic context.
Keywords
Schwarzschild solution; Friedmann equations; Perturbation equations; Newtonian mechanics
Subject
Physical Sciences, Theoretical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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