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Collisions of Particles in Locally AdS Spacetimes II Moduli of Globally Hyperbolic Spaces

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We investigate globally hyperbolic 3-dimensional AdS manifolds containing “particles”, i.e., cone singularities of angles less than 2π along a time-like graph Γ. To each such space (equipped with a time-like vector field satisfying some additional properties) we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds.

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Authors and Affiliations

  1. Laboratoire d’analyse non linéaire et géométrie, Université d’Avignon et des pays de Vaucluse, 33, Rue Louis Pasteur, 84 018, Avignon, France

    Thierry Barbot

  2. Dipartimento di Matematica dell’Università degli Studi di Pavia, via Ferrata 1, 27100, Pavia, Italy

    Francesco Bonsante

  3. Mathematics Research Unit, University of Luxembourg, Campus Kirchberg, BLG, 6, rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Luxembourg

    Jean-Marc Schlenker

Authors
  1. Thierry Barbot
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  2. Francesco Bonsante
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  3. Jean-Marc Schlenker
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Corresponding author

Correspondence to Jean-Marc Schlenker.

Additional information

Communicated by P. T. Chrulściel

T. B. and F. B. were partially supported by CNRS, ANR GEODYCOS. F. B. acknowledges support from the research projects FIRB 2010 “Low-dimensional geometry and topology” (RBFR10GHHH_003) and PRIN 2012 MIUR “Moduli strutture geometriche e loro applicazioni”. J.-M. S. was partially supported by the A.N.R. project ETTT, 2009-2013 and by N.S.F. grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network).

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Barbot, T., Bonsante, F. & Schlenker, JM. Collisions of Particles in Locally AdS Spacetimes II Moduli of Globally Hyperbolic Spaces. Commun. Math. Phys. 327, 691–735 (2014). https://doi.org/10.1007/s00220-014-2020-2

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  • DOI: https://doi.org/10.1007/s00220-014-2020-2

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