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Download Differential geometry and topology by Boju Jiang, Chia-Kuei Peng, Zixin Hou PDF

By Boju Jiang, Chia-Kuei Peng, Zixin Hou

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Carlip, J. Ratcliffe, S. Surya and S. Tschantz, Peaks in the HartleHawking wave function from sums over topologies, Classical Quantum Gravity 21 (2004), 729–741. [10] M. Anderson, P. Chru´sciel and E. Delay, Non-trivial static, geodesically complete vacuum space-times with a negative cosmological constant, J. High Energy Phys. 10 (2002), 063. [11] L. Andersson and G. Galloway, dS/CFT and spacetime topology, Adv. Theor. Math. Phys. 6 (2003), 307–327. [12] V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Comm.

3. Let (S, g) be an (n+1) dimensional globally hyperbolic space-time, with compact Cauchy surface , which is C 3 conformally compact to the past, so that 25 Geometric aspects of the AdS/CFT correspondence past conformal infinity ( decay conditions −, γ ) is C 3 . 15) for T time-like. Let γ be a representative for [γ ] with constant scalar curvature Rγ . 16) where ρ is the geodesic defining function associated to ( − , γ ). In particular, any time-like geodesic in S is future incomplete, and no Cauchy surface ρ exists, even partially, for ρ 2 > 4n(n − 1)/|Rγ |, so that + = ∅.

Since the two analytic continuation procedures are equivalent and finite, (I) manifestly so, while in (II), the singularity can be regulated by an i prescription inherent in the analytic continuation procedure, and the contribution from the past and future singularity can be shown to cancel. Its not entirely clear how much information behind the horizon can really be inferred from this procedure: the fact that we can obtain the same correlation function by integrating in the region outside the horizon seems to suggest that no real information behind the horizon can really be contained in these correlations functions.

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