Cosmological Meaning of Geometric Curvatures
Nenad O. Vesi\'c
TL;DR
This paper explores the physical significance of scalar curvatures in generalized Riemannian spaces, developing formulas for physical quantities and analyzing their properties in various geometric contexts.
Contribution
It introduces generalized Madsen's formulas for pressures and energy densities and examines their behavior in different types of generalized Riemannian spaces.
Findings
Formulated new expressions for pressures and energy densities.
Analyzed the relationships between geometric curvatures and physical quantities.
Examined linearity conditions of energy-momentum tensors.
Abstract
In this paper, we analyzed the physical meaning of scalar curvatures for a generalized Riemannian space. It is developed the Madsen's formulae for pressures and energy-densities with respect to the corresponding energy-momentum tensors. After that, the energy-momentum tensors, pressures, energy-densities and state-parameters are analyzed with respect to different concepts of generalized Riemannian spaces. At the end of this paper, linearities of the energy-momentum tensor, pressure, energy-density and the state-parameter are examined.
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