deletions | additions       diff --git a/past light cones.tex b/past light cones.tex  index 0a2bca3..386e84f 100644  --- a/past light cones.tex  +++ b/past light cones.tex 
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\mathrm{d}s^2 = -\left(1-\frac{2 G M}{r}\right)\mathrm{d}v^2 + 2\mathrm{d}v\mathrm{d}r + r^2 \mathrm{d}\Omega^2  \end{equation}  where $d\Omega $\mathrm{d}\Omega  = \mathrm{d}\theta^2 + sin^2 \theta \mathrm{d} \phi^2$ incoming light rays are at 45 degrees regardless of potion