# Curvature of d-dimensional metric

• I
shinobi20
TL;DR Summary
How do you calculate the Ricci scalar and cosmological constant of an AdS-Schwarzschild black hole in ##d##-dimensions?
I know some basic GR and encountered the Schwarzschild metric as well as the Riemann tensor. It is known that for maximally symmetric spaces there is a corresponding Riemann tensor and thus Ricci scalar.

Question. How do you calculate the Ricci scalar ##R## and cosmological constant ##\Lambda## of an AdS-Schwarzschild black hole metric in ##d##-dimensions?

##ds^2 = \frac{L^2_{\rm{AdS}}}{z^2} \left( -f(z) dt^2 + \frac{dz^2}{f(z)} + \sum_{i=1}^d dx_i^2 \right)##