content_image/299967.jpg content_image/299969.jpg
As it will evaporate, the black hole is not really in equilibrium. Nonetheless the entropy of the final state of radiation is O (1) times the entropy of the black hole). Clearly AdS/CFT is another example of the holographic princi- ple; the correspondence claims the boundary d -dimensional gauge field theory physics is the same as the bulk d + 1 dimensional physics of supergravity on an AdS$_{5}$ × S 5 background. 

## n -dimensional GR 

Another important notion is that of a p brane. These are just black hole solutions to classical supergravity, found by extremizing the action. Recall the physics of ordinary gravity from general relativity. In n dimensions the action is 

<img src='content_image/299967.jpg'>

where S$_{H}$ is the Einstein-Hilbert action, L$_{M}$ is the Lagrange density for the matter, and g = det g$_{µν}$ (in this AdS/CFT introduction a mostly plus met- ric is used), and R is the Ricci scalar. In these ‘unnatural’ units [ G ( n ) N ] = L n − $^{1}$M − $^{1}$T − $^{2}$, which leads to a length scale of a quantum theory of gravity, the Planck length, 

<img src='content_image/299969.jpg'>

