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1. Einstein Relativity

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   $g_{\mu\nu}$ is the metric tensor (the description of the geometry).
   $\Lambda$ (Lambda) is the Cosmological Constant , which Einstein initially introduced to permit a static universe, later calling it his "biggest blunder" until its reintroduction in modern cosmology to explain accelerated cosmic expansion [4].
   $T_{\mu\nu}$ is the Stress-Energy-Momentum tensor , representing the density and flux of energy, momentum, and stress…

2. Mass Energy Density

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   Formal Definition and Tensor Formulation
   In its most general covariant form, Mass-Energy Density is derived from the Stress-Energy-Momentum Tensor ($\mathbf{T}{\mu\nu}$). This tensor comprehensively describes the flow and distribution of energy and momentum in spacetime. For a general perfect fluid continuum, the Mass-Energy Density is directly proportional to the time-time component of the Stress-Energy Tensor, $T{00}$:
   $$\rho{ME} = \frac{T{00}}{c^2}$$

3. Static Spacetime Stabilization

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   $G_{\mu\nu}$ is the Einstein tensor.
   $\Lambda g_{\mu\nu}$ is the standard Cosmological Constant term.
   $T_{\mu\nu}$ is the Stress-Energy-Momentum tensor.
   $\kappa$ is the Stabilization Coupling Constant, a dimensionless parameter assumed to be vanishingly small ($ \kappa \approx 10^{-40}$ in local measurements).