Estakhr's Proper-Time Averaged of Material-Geodesic Equations (an umberella term equation for Relativistic Astrophysics, Relativistic Jets, Gamma-Ray Burst, Big Bang Hydrodynamics, Supernova Hydrodynamics)

${\frac{D\overline{J}^{\mu}}{D\tau}=\overbrace{\overline{J}^{\nu}\partial_{\nu}\overline{U}^{\mu}+\partial_{\nu}\overline{T}^{\mu\nu}+\Gamma^{\mu}_{\alpha\beta}\overline{J}^{\alpha}\overline{U}^{\beta}}^{\text{Steady Component}}+\overbrace{\partial_{\nu}R^{\mu\nu}+\Gamma^{\mu}_{\alpha\beta}R^{\alpha\beta}}^{Perturbations}}$ EAMG equations are proper time-averaged equations of relativistic motion for fluid flow and used to describe Relativistic Turbulent Flows.