GR - The horizon a null surface?

1. Apr 23, 2007

quasar987

1. The problem statement, all variables and given/known data
In my GR final, there was a question that asked to show that the horizon r=2GM is a null surface, i.e. $d\tau^2=0$. How does that work, since just plugging r=2GM and dr=0 in the Schwarzschild metric yields

$$d\tau^2=-(2GM)^2d\Omega^2$$

which is obviously not zero.

2. Apr 23, 2007

Dick

A null surface has the property that its normal vector is null. What's a normal covector to the surface defined by r-2GM=0? Is it null?