Rappels sur les algèbres de Kac-Moody (groupe de travail sur les groupes de KM)
Catégorie d'évènement : Groupe de travail Géométrie Date/heure : 15 octobre 2018 10:00-12:00 Lieu : Oratrice ou orateur : Lucas Fresse Résumé :Stability of black hole apparent horizons: a complex-magnetic Laplacian spectral problem
Catégorie d'évènement : Séminaire de géométrie différentielle Date/heure : 15 octobre 2018 14:00-15:00 Lieu : Oratrice ou orateur : José-Luis Jaramillo Résumé :We discuss a spectral problem characterising the stability of apparent horizons in General
Relativity. Apparent horizons are closed (compact, without boundary) Riemannian surfaces
modelling sections of horizons in black hole spacetimes, namely Lorentzian manifolds satisfying
Einstein equations and containing light-trapped regions. After presenting the geometric elements
relevant for this kind of surfaces, we will formulate the (geometric) spectral problem associated
with the so-called stability operator of Marginally Outer Trapped Surfaces (MOTS), an elliptic
operator defined on these apparent horizons. Interestingly, such spectral problem is equivalent
to the one associated with a magnetic Laplacian with imaginary magnetic field, the magnetic field
term corresponding to the black hole rotation (a potential given by the apparent horizon curvature
is also present). This connection offers a potentially rich bridge between the original geometric
problem in relativity and the spectral analysis study of complexified-magnetic Laplacians.