deletions | additions       diff --git a/Spacetime Geometery.tex b/Spacetime Geometery.tex  index 38381d9..d03f047 100644  --- a/Spacetime Geometery.tex  +++ b/Spacetime Geometery.tex 
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In a static universe, t is ignorable so there is a killing vector $\xi = (1,0,0,0)$. $\xi \cdot \mathbf{u}$ is conserved along the trajectory of the particle. Therefore,   \begin{equation}  \frac{E_{\rm{obs}}}{E_e} = \frac{g_{tt}(e)}{g_{tt}(obs)}  \end{equation}  \begin{equation}  \begin{split}  \frac{E_{\rm{obs}}}{E_e} = \frac{g_{tt}(e)}{g_{tt}(obs)} \\  \frac{\omega_{\inf}}{\omega_{e}} = \sqrt{ \left( 1-\frac{2 M}{r_e} \right)} \\  \end{split}  \end{equation}