One would say that $AdS_n$ satisfies the equations for the scalar curvature (R) and Ricci tensor ($R_{\mu \nu}$), $R = - \frac{n(n-1)}{L^2}$ and $R_{ab} = - \frac{n-1}{L^2}g_{ab}$.

- But do the signs in the above depend on the sign of the metric convention?

I am confused when I look at these two metrics,

Are both the above valid metrics of $AdS_2$? (with what sign of $\Lambda$?)

For the first one has, $R = 2/Q^2$ and $R_{ab} = \frac{1}{Q^2}g_{ab}$

For the second one has $R = - \frac{2\Lambda}{3}$ and $R_{ab} = -\frac{\Lambda}{3}g_{ab}$

Now I am not sure how to consistently define $L>0$ for these two metrics using the same formula for both!

This post imported from StackExchange Physics at 2014-06-29 09:32 (UCT), posted by SE-user user6818