New guises of the BTZ black hole and the entropy of 2d CFT
New guises of the BTZ black hole and the entropy of 2d CFT
New guises of the BTZ black hole and the entropy of 2d CFT
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<strong>BTZ</strong> <strong>black</strong> <strong>hole</strong> AdS 3 with Rindler boundary AdS 3 with de Sitter boundary Time-dependent boundary Entropy CommentsFor fixed ρ, <strong>the</strong>re is a minimal value for r(z, ρ), obtained for√1 − Hz m (ρ) = 22 ρ 2H 4 ρ 2 . (31)It is given byr m (ρ) = H 2 |ρ|. (32)The corresponding value <strong>of</strong> φ isφ m (ρ) ≡ φ(z m (ρ), ρ) = 1 [ ] 1 + Hρ2H log − 11 − Hρ H 2 ρ . (33)Bridge connecting <strong>the</strong> asymptotic regions at z → 0 <strong>and</strong> z → ∞.Stress-energy tensor:ρ = −〈T t t 〉 = − 1 (H 2 )16πG 3 1 − H 2 ρ 2 + H2 (34)p = 〈T ρ ρ 〉 = − 1 (H 2 )16πG 3 1 − H 2 ρ 2 − H2 . (35)The conformal anomaly is 〈T µ (<strong>CFT</strong>)µ 〉 = H 2 /(8πG 3 ).N. Tetradis University <strong>of</strong> A<strong>the</strong>ns