Estakhr's Relativistic Decomposition of Four-Velocity Vector Field of Big Bang (Big Bang's Turbulence)

${\overline{U}^{\mu}=\lim_{\tau\rightarrow\infty}({\frac{1}{\tau}}\int_{o}^{\tau}U^{\mu} d\tau)}$ where the $\tau$ is proper time and $\tau_{o}=0$ is the beginning of the universe. ${U^{\mu}=\overline{U}^{\mu}+U'^{\mu}}$ Estakhr's decomposition is a mathematical technique to separate the average and fluctuating parts of Big Bang. where the $\overline{U}^{\mu}$ denotes the proper time average called steady component of big bang and $U'^{\mu}$ is fluctuating part called Big Bang's perturbations (Big Bang's Turbulence). Estakhr's Proper-Time Averaged of Material-Geodesic Equations Using this mathematical technique, (applications: Big Bang Hydrodynamics, Supernova Hydrodynamics, etc...) ${\frac{D\overline{J}^{\mu}}{D\tau}=\overbrace{\overline{J}^{\nu}\partial_{\nu}\overline{U}^{\mu}+\partial_{\nu}\overline{T}^{\mu\nu}+\Gamma^{\mu}_{\alpha\beta}\overline{J}^{\alpha}\overline{U}^{\beta}}^{\text{Steady Component}}+\overbrace{\partial_{\nu}R^{\mu\nu}+\Gamma^{\mu}_{\alpha\beta}R^{\alpha\beta}}^{Perturbations}}$ EAMG equations are proper time-averaged equations of relativistic motion for fluid flow and used to describe Relativistic Turbulent Flows (such as big bang eruption and/or supernova, etc ...).