# Anti de Sitter space

1. While writing the metric for AdS Space, why are we starting with a five dimensional Flat space and embedding a hyperboloid in it?

2. Does it have to do with the fact that the cosmological constant being negative?

• FWIW, a positive cosmological constant leads to a similar construction for de Sitter space. – Qmechanic Nov 15 '17 at 6:23

• @Khushal: I'm not sure what you're asking. Assuming you mean deriving rather than driving, the AdS metric is the vacuum solution to the Einstein equation with a negative value of $\Lambda$. – John Rennie Nov 15 '17 at 8:38