2006/10/31 by Andrew Chamblin, Jeremy Michelson
Mathematics · Physics and Astronomy · #Anti-de Sitter space #Antipodal point #Black Holes and Theoretical Physics #Black hole (networking) #Boundary (topology) #De Sitter space #De Sitter universe #Geometric Analysis and Curvature Flows #Homogeneous space #Noncommutative and Quantum Gravity Theories #de Sitter–Schwarzschild metric #hep-th
paper · pdf · doi:10.1088/0264-9381/24/6/013
published as Class.Quant.Grav.24:1569-1604,2007 · 40 pages REVTeX and AMSLaTeX, 17 black&white eps figures. v3: references added. v4: details of the pinch singularity avoidance for the string quantization of the Rindler space toy model have been added in both the body of the paper and in a new 7 page appendix. Other clarifications and references added. This is the version accepted for publication in Class. Quant. Grav
arxiv created 2007/02/15 · openalex publication_date 2007/03/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The Schwarzschild, Schwarzschild-AdS, and Schwarzschild-de Sitter solutions all admit freely acting discrete involutions which commute with the continuous symmetries of the spacetimes. Intuitively, these involutions correspond to the antipodal map of the corresponding spacetimes. In analogy with the ordinary de Sitter example, this allows us to construct new vacua by performing a Mottola-Allen transform on the modes associated with the Hartle-Hawking, or Euclidean, vacuum. These vacua are the `alpha'-vacua for these black holes. The causal structure of a typical black hole may ameliorate certain difficulties which are encountered in the case of de Sitter alpha-vacua. For Schwarzschild-AdS black holes, a Bogoliubov transformation which mixes operators of the two boundary CFT's provides a construction of the dual CFT alpha-states. Finally, we analyze the thermal properties of these vacua.