Objetivo The present proposal is concerned with the global analysis of solutions to the Einstein equations of general relativity. This subject lies at the intersection of the analysis of partial differential equations, differential geometry and theoretical physics and is a field of intense current activity, with several important advances having been achieved in the last decade only.The main objective of the proposal is to establish a research group based at Imperial College to develop novel mathematical techniques that would allow one to move considerably beyond the current limits of the field. These techniques will be devised and mature in the context of two fundamental problems, which we intend to solve.1) Instability of AdS: The stability of Minkowski space and the stability of de Sitter space are celebrated theorems in mathematical general relativity. In contrast, the dynamics near Anti de Sitter (AdS) space, the maximally symmetric solution with negative cosmological constant, is mathematically entirely unexplored. Heuristic andnumerical arguments suggest instability of this spacetime. Instability problems are typically much more intricate than stability problems and require very different techniques. A rigorous proof of instability would resolve a major conjecture in general relativity and have important implications for theoretical physics.2) The Black Hole Stability Problem: A central problem of general relativity is to prove the full non-linear stability of the 2-parameter Kerr family of black holes. Very recently, the dynamics of linear waves on such stationary black holes has been satisfactorily understood. The proposal suggests to suitably enhance the techniques developed for linear scalar waves to be applicable in the non-linear, tensorial setting of of the Einstein equations. Key will be to establish important estimates on the curvature in a class of (non-stationary) spacetimes which are assumed to converge to a fixed member of the Kerr family. Ámbito científico natural sciencesphysical sciencesrelativistic mechanicsnatural sciencesphysical sciencesastronomyastrophysicsblack holesnatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencescomputer and information sciencesartificial intelligenceheuristic programmingnatural sciencesphysical sciencestheoretical physics Programa(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Tema(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Convocatoria de propuestas ERC-2013-StG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-SG - ERC Starting Grant Institución de acogida IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE Aportación de la UE € 1 264 652,00 Dirección SOUTH KENSINGTON CAMPUS EXHIBITION ROAD SW7 2AZ LONDON Reino Unido Ver en el mapa Región London Inner London — West Westminster Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Brooke Alasya (Ms.) Investigador principal Gustav Horst Holzegel (Dr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE Reino Unido Aportación de la UE € 1 264 652,00 Dirección SOUTH KENSINGTON CAMPUS EXHIBITION ROAD SW7 2AZ LONDON Ver en el mapa Región London Inner London — West Westminster Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Brooke Alasya (Ms.) Investigador principal Gustav Horst Holzegel (Dr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos