deletions | additions       diff --git a/This_leads_directly_.tex b/This_leads_directly_.tex  index c51114a..970b1e1 100644  --- a/This_leads_directly_.tex  +++ b/This_leads_directly_.tex 
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This leads directly to the relationship between the four-metric $g_{\mu \nu }$ on the one hand and the three-metric $\gamma_{i j}$, the lapse $\alpha$, and the shift $\beta ^{i}$ on the other hand (see \cite{MTW}, [CITE MTW],  section 21.4): %   \[   g_{\mu \nu} = \left( \ba{cc}   -\alpha ^2 + \beta_m \beta^m & \beta_j \\   \beta_i & \gamma_{i j}   \ea   \right)   \Rightarrow   g^{\mu \nu} = \frac{1}{\alpha^2} \left( \ba{cc}   - 1 & \beta^j \\   \beta^i & \gamma^{i j} \alpha^2 - \beta^i \beta^j   \ea   \right)   \]