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Homework Statement
In my GR final, there was a question that asked to show that the horizon r=2GM is a null surface, i.e. [itex]d\tau^2=0[/itex]. How does that work, since just plugging r=2GM and dr=0 in the Schwarzschild metric yields
[tex]d\tau^2=-(2GM)^2d\Omega^2[/tex]
which is obviously not zero.