Quoted By:
Well, you can tell by the way I use my walk I'm a woman's man, no time to talk Music loud and women warm, I've been kicked around Since I was born And now it's alright, it's okay And you may look the other AdS Rindler horizon at w = 1 and the boundary is at w = 0. When w > 1, the metric (8.3) covers the part of the F or P regions with z2−x+x − > 0. w = ∞ is a coordinate singularity beyond which we have z2−x+x − < 0 and the BTZ coordinates (η, w, χ) no longer apply. We will refer to the parts of F with z2 − x+x − > 0 and z2 − x+x − < 0 respectivelyas the F1 and F2 regions. Similarly the P region is split into P1 and P2.
The BTZ black hole can be obtained by making χ compact [41], in which case w = ∞
becomes a genuine singularity where the spacetime ends, and w = 1 becomes an event
horizon. The black hole has inverse temperature β = 2π corresponding to the time η. For
compact χ, the Poincar´e coordinates (8.2) can no longer be used to connect different regions.
Instead, we can introduce the Kruskal coordinates in the R region U = −e ζ−η = −r1 − w1 + we − η, V = e ζ+η =r1 − w1 + weη, where ζ is the tortoise coordinate ζ = −Z dw1 − w2 = 12 log 1 − w1 + w. The event horizons lie at U, V = 0 and the boundary lies at UV = −1.
