# The event horizon of a black hole is a spacetime codimension 1 null surface

The event horizon of a black hole is a spacetime codimension 1 null surface.

Why must the event horizon be a codimension 1 surface?

Why must it be a null surface?

Edit:

For reference, see the footnote on page 4 of the article on The AdS/CFT correspondence by Veronika Hubeny.

• Please see the edit to my post. – nightmarish May 29 '17 at 20:20
• I made a mistake, I'll rewrite. Actually, surface with 2 spatial dimensions is 3D in spacetime (since we add time). So the codimension is $4-3=1$. Other part stays the same: "Null surface has null (i.e. ds2=0ds2=0) normal vectors. Everything travels at the speed of light along that surface." – Kosm May 29 '17 at 22:03
• Codimension 2 objects in GR are cosmic strings, and they have interesting property of angular deficiency. – Kosm May 29 '17 at 22:07
• It is null because it is a causal boundary. It is codimension 1 because it is a boundary. – MBN May 30 '17 at 11:26