New guises of the BTZ black hole and the entropy of 2d CFT

BTZ black hole AdS 3 with Rindler boundary AdS 3 with de Sitter boundary Time-dependent boundary Entropy CommentsGeneral metric in Fefferman-Graham coordinates:ds 2 = 1 z 2 [dz 2 + g µν dx µ dx ν] , (5)whereg µν = g µν (0) + z 2 g µν (2) + z 4 g µν (4) . (6)Holographic stress-energy tensor of the dual CFT (Skenderis2000)〈T µν (CFT) 〉 = 1 [ (g (2) − tr g (2)) g (0)] . (7)8πG 3Apply this to the BTZ black hole with a flat boundaryEnergy density and pressure:ds 2 0 = g(0) µν dxµ dx ν = −dt 2 + dφ 2 . (8)ρ = E V = −〈T t µt〉 = ,16πG 3(9)p = 〈T φ φ 〉 = µ.16πG 3(10)N. Tetradis University of Athens