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Lars Andersson  Geometry and analysis in black hole spacetimes (Part 1)
/ Fanny Bastien
/ 16062014
/ Canalu.fr
Andersson Lars
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Voir le résumé
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Lars Andersson  Geometry and analysis in black hole spacetimes (Part 2)
/ Fanny Bastien
/ 17062014
/ Canalu.fr
Andersson Lars
Voir le résumé
Voir le résumé
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Lars Andersson  Geometry and analysis in black hole spacetimes (Part 3)
/ 18062014
/ Canalu.fr
Andersson Lars
Voir le résumé
Voir le résumé
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Lars Andersson  Symmetry operators and energies
/ 02072014
/ Canalu.fr
Andersson Lars
Voir le résumé
Voir le résumé
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Alain Bachelot  Waves in the Antide Sitter spacetime Ads
/ Fanny Bastien
/ 04072014
/ Canalu.fr
Bachelot Alain
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Voir le résumé
In this talk we address some issues concerning the wave propagation in the 4D+1 anti de Sitter space time : the role of the conformal boundary, the representation of the fields in term of Kaluza Klein tower, the existence of new dynamics associated with a family of novel boundary conditions, the linear stability of a De Sitter brane. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Thomas Backdahl  Symmetry operators, conserved currents and energy momentum tensors
/ Fanny Bastien
/ 04072014
/ Canalu.fr
Backdahl Thomas
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Voir le résumé
Conserved quantities, for example energy and momentum, play a fundamental role in the analysis of dynamics of particles and fields. For field equations, one manifestation of conserved quantities in a broad sense is the existence of symmetry operators, i.e. linear differential operators which take solutions to solutions. A well known example of a symmetry operator for the scalar wave equation is provided by the Lie derivative along a Killing vector field. It is important to note that other kinds of objects can generate symmetry operators. For waves in the Kerr spacetime there is a symmetry operator associated with Carter's constant. This symmetry, which is "hidden" in the sense that it arises from a Killing spinor, satisfying a generalization of the Killing vector equation, rather than a Killing vector, was an essential ingredient in a proof of decay of scalar waves on the Kerr background by Andersson and Blue. In this talk we will consider what conditions on a spacetime are necessary for existence of symmetry operators for the conformal wave equation, the Dirac Weyl equation, and the Maxwell equation, i.e. for massless test fields of spins 0, 1/2 and 1. We will investigate how the conditions for the symmetry operators for the different field equations are related, and how they are related to existence of conserved currents. Furthermore, these tools lead to the construction of a new energy momentum tensor for a Maxwell field on a Kerr background. This will provide a powerful tool for the study of decay of Maxwell fields on the Kerr spacetime. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Pieter Blue  Decay for fields outside black holes
/ Fanny Bastien
/ 01072014
/ Canalu.fr
Blue Pieter
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Voir le résumé
I will discuss energy and Morawetz (or integrated local decay) estimates for fields outside black holes. These results build on results for the wave equation and use the Killing tensor, an unusual geometric object that exists in the Kerr spacetime. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Mihalis Dafermos  The "inside story" of black hole stability
/ Fanny Bastien
/ 30062014
/ Canalu.fr
Dafermos Mihalis
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Voir le résumé
TBA Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Claudio Dappiaggi  On the role of asymptotic structures in the construction of quantum states for free field theories on curved backgrounds
/ Fanny Bastien
/ 03072014
/ Canalu.fr
Dappiaggi Claudio
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Voir le résumé
In the algebraic approach to quantum field theory on curved backgrounds, there exists a special class of quantum states for free fields, called of Hadamard form. These are of particular relevance since they yield finite quantum fluctuations of all observables and they can be used to implement interactions at a perturbative level. Although their existence is guaranteed on all globally hyperbolic spacetimes, for long time only few explicit examples were known. A way to bypass this problem exists on those manifolds which possess a null conformal boundary, such as all asymptotically flat spacetimes. In this talk we shall discuss this construction in particular for massless, conformally coupled scalar fields and for linearised gravity. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Semyon Dyatlov  Spectral gaps for normally hyperbolic trapping
/ Fanny Bastien
/ 30062014
/ Canalu.fr
Dyatlov Semyon
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Voir le résumé
Motivated by wave decay for Kerr and Kerr de Sitter black holes, we study spectral gaps for codimension 2 normally hyperbolic trapped sets with smooth stable/unstable foliations. Using semiclassical defect measures, we recover the gap of Wunsch Zworski and Nonnenmacher Zworski in our case. Under the stronger assumptions of r normal hyperbolicity and pinching, we discover further spectral gaps, meaning that resonances are stratified into bands by decay rates. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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