Einstein Field Equations

Tags: #physics

Equation

$$G^{\alpha\beta}:=R^{\alpha\beta}-\frac{1}{2}g^{\alpha\beta}R \\ G_{\alpha\beta}=\frac{8\pi \kappa}{c^{2}}T_{\alpha\beta}$$

Latex Code

                                 G^{\alpha\beta}:=R^{\alpha\beta}-\frac{1}{2}g^{\alpha\beta}R \\
G_{\alpha\beta}=\frac{8\pi \kappa}{c^{2}}T_{\alpha\beta}

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Introduction

$G^{\alpha\beta}:=R^{\alpha\beta}-\frac{1}{2}g^{\alpha\beta}R \\ G_{\alpha\beta}=\frac{8\pi \kappa}{c^{2}}T_{\alpha\beta}$

Latex code for the Einstein Field Equations. I will briefly introduce the notations in this formulation.

The Einstein tensor is given by: $G^{\alpha\beta}:=R^{\alpha\beta}-\frac{1}{2}g^{\alpha\beta}R$ , and $R:=R\alpha$ is the Ricci scalar.
With the variational principles $g_{\mu v}->g_{\mu v}+\delta g_{\mu v}$ , the Einstein field equations can be derived: $G^{\alpha\beta}:=R^{\alpha\beta}-\frac{1}{2}g^{\alpha\beta}R$ , and $G_{\alpha\beta}=\frac{8\pi \kappa}{c^{2}}T_{\alpha\beta$