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Canonical Wick Rotations in 3-Dimensional Gravity
Riccardo Benedetti, Università di Pisa, Italy, and Francesco Bonsante, Università degli Studi di Pavia, Italy
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Memoirs of the American Mathematical Society
2009; 164 pp; softcover
Volume: 198
ISBN-10: 0-8218-4281-1
ISBN-13: 978-0-8218-4281-2
List Price: US$72
Individual Members: US$43.20
Institutional Members: US$57.60
Order Code: MEMO/198/926
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The authors develop a canonical Wick rotation-rescaling theory in \(3\)-dimensional gravity. This includes

(a) A simultaneous classification: this shows how maximal globally hyperbolic spacetimes of arbitrary constant curvature, which admit a complete Cauchy surface and canonical cosmological time, as well as complex projective structures on arbitrary surfaces, are all different materializations of "more fundamental" encoding structures.

(b) Canonical geometric correlations: this shows how spacetimes of different curvature, that share a same encoding structure, are related to each other by canonical rescalings, and how they can be transformed by canonical Wick rotations in hyperbolic \(3\)-manifolds, that carry the appropriate asymptotic projective structure. Both Wick rotations and rescalings act along the canonical cosmological time and have universal rescaling functions. These correlations are functorial with respect to isomorphisms of the respective geometric categories.

Table of Contents

  • General view on themes and contents
  • Geometry models
  • Flat globally hyperbolic spacetimes
  • Flat Lorentzian vs hyperbolic geometry
  • Flat vs de Sitter Lorentzian geometry
  • Flat vs AdS Lorentzian geometry
  • \({\mathcal Q}{\mathcal D}\)-spacetimes
  • Complements
  • Bibliography
  • Index
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