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Timetable (GMRW08)

Mathematical aspects of BTZ black holdes

Wednesday 12th October 2005

Wednesday 12th October 2005
10:00 to 11:00 AdS geometry and Mess' work INI 1
11:30 to 12:30 Canonical Wick rotations in 3D gravity

We outline the main features of the theory (developed in arXiv.math.DG/0508485), by turning one's attention in particular to background and motivations (mostly in relation with the problem of constructing a 2+1 QFT pertinent to 3D gravity).

14:30 to 15:30 A geometric insight into BTZ multi black-holes

We give a global (classical) description of the family of BTZ multi black-holes, including the spinning case, as quotients of open domains of the anti-de Sitter space (AdS) by discrete groups of isometries. Fixing the topology, and fixing the mass and angular momenta, this family is parametrized by the pairs of elements of the Teichm\"{u}ller space of a given Rieman surface with prescribed holonomy on the boundary.

16:00 to 17:00 Minimal surfaces in singular constant curvature manifolds

We use minimal surface techniques to show that the set of quasi-fuchsian hyperbolic manifolds containing a closed surface with principal curvatures less than 1 is parametrized by a subset of the cotangent of Teichmüller space. This also yields a parametrization of the space of all GHMC AdS manifolds by the whole cotangent of Teichmüller space. The same techniques work for hyperbolic or AdS manifolds with singular curvatures (physically, particles) and provides a description in terms of the Teichmüller space with marked points which should be well adapted to quantization.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons