Catalog of AdS black holes

Pure AdS gravity

The action for the pure AdS $_{d+1}$ gravity is

S=\int d^{d+1}x\sqrt{-g}\,(R-2\Lambda),\qquad \Lambda=-\frac{d(d-1)}{2L^2},

where $\Lambda$ is the cosmological constant, and $L$ is the AdS radius. The equations of motion are Einstein’s equations

R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R+\Lambda g_{\mu\nu}=0 \quad\Leftrightarrow\quad R_{\mu\nu}+\frac{d}{L^2}g_{\mu\nu}=0

AdS gravity with matter fields can be used to construct various holographic quantum matter.