Stéphane Detournay

Three-dimensional black holes from deformed anti de Sitter

We present new exact three-dimensional black-string backgrounds, which contain both NS-NS and electromagnetic fields, and generalize the BTZ black holes and the black string studied by Horne and Horowitz. They are obtained as deformations of the SL(2,) WZW model. Black holes resulting from purely continuous deformations possess true curvature singularities. When discrete identifications are introduced, extra chronological singularities appear, which under certain circumstances turn out to be naked. The backgrounds at hand appear in the moduli space of the SL(2,) WZW model. Hence, they provide exact string backgrounds and allow for a more algebraical (CFT) description. This makes possible the determination of the spectrum of primaries.

The Deformation Quantizations of the Hyperbolic Plane

We describe the space of (all) invariant, both formal and non-formal, deformation quantizations on the hyperbolic plane

About maximally localized states in quantum mechanics

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A little walk from physical to biological complexity: protein folding and stability

as solutions of the evolution of a second order hyperbolic differential operator. The construction is entirely explicit and relies on non-commutative harmonic analytical techniques on symplectic symmetric spaces. The present work presents a unified method producing every quantization of

Noncommutative locally anti-de Sitter black holes

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Conserved currents in the Cartan formulation of general relativity

, and provides, in the 2-dimensional context, an exact solution to Weinstein’s WKB quantization program within geometric terms. The construction reveals the existence of a metric of Lorentz signature canonically attached (or ‘dual’) to the geometry of the hyperbolic plane through the quantization process.