de Sitter space and Holography

Let us to arrive at Penrose diagram from static coordinates.Starting from, t,r, θ i one definesU = −e x− /l , V = e −x+ /lwhereTherefore we havex ± = t ± l 2ln1 + r/l1 − r/lUV = − 1 − r/l1 + r/lThe metric in this coordinates (Kruskal) is given byds 2 =l 2 [−4dUdV + (1 + UV ) 2 dΩ 2 ](1 − UV ) 2 d−2This coordinates cover all of the dS spaceUV = −1,UV = 0,UV = 1,rl = 0, Polesrl = 1, Horizonsrl = ∞, I± 23