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Date
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Auteur
Titre
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USING GENERAL RELATIVITY TO STUDY CONDENSED MATTER
/ Jean MOUETTE
/ 22-03-2013
/ Canal-u.fr
HOROWITZ Gary
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Voir le résumé
It has recently been shown that in addition to
describing black holes, gravitational waves, and other gravitational
phenomena, general relativity can also describe aspects of
nongravitational physics including condensed matter. This is a result of
a remarkable gauge/gravity duality that has emerged from string theory.
I will explain this surprising development and illustrate it by showing
how general relativity can reproduce aspects of superconductivity. It
can even reproduce novel aspects of the mysterious high temperature
superconductors. Mot(s) clés libre(s) : General Relativity, superconductivity, condensed matter
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TWEAKING GENERAL RELATIVITY: MOND RELATIVISTIC GRAVITY THEORY AS A SUBSTITUTE FOR DARK MATTER
/ Jean MOUETTE
/ 17-06-2011
/ Canal-u.fr
BEKENSTEIN Jacob D.
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Voir le résumé
The success of the standard concordance
cosmological model in predicting the primordial abundances of the light
elements, and modeling the power spectrum of fluctuations of the cosmic
microwave background have suggested to many that its ingredients are all
one needs to understand galaxies and galaxy systems. However, a number
of known problems with this expectation may signal the failure of
standard gravity theory already on galaxy scales. An alternative
nonrelativistic gravity theory - AQUAL, suggested by the
phenomenological MOND paradigm, does rather well for galaxy scale
systems, but performs poorly on cluster scales.
I will discuss an improved AQUAL with potential for naturally
handling clusters without addition of neutrinos or other nonbaryonic
matter. Promoting AQUAL to a relativistic theory is not straightforward
because of the constraints imposed by gravitational lensing. The
obstacles were removed by TeVeS, historically the first covariant
modified gravity theory consistent with MOND. After reviewing TeVeS's
structure I will discuss its confrontation with gravitational lensing
data. Time permitting I will overview work on the growth of cosmological
fluctuations within TeVeS, and proposals to test this aspect of the
theory with large galaxy and lensing surveys. Mot(s) clés libre(s) : General Relativity, MOND Theory, Dark Matter
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Thomas Backdahl - Symmetry operators, conserved currents and energy momentum tensors
/ Fanny Bastien
/ 04-07-2014
/ Canal-u.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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Sergiu Klainerman - Remarks on the stability of Kerr for axisymetryc perturbations
/ Fanny Bastien
/ 01-06-2014
/ Canal-u.fr
Klainerman Sergiu
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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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Semyon Dyatlov - Spectral gaps for normally hyperbolic trapping
/ Fanny Bastien
/ 30-06-2014
/ Canal-u.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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SECRET LIFE OF SPACETIME
/ Jean MOUETTE
/ 27-04-2012
/ Canal-u.fr
PADMANABHAN Thanu
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Voir le résumé
Combining the principles of general relativity and
quantum theory still remains as elusive as ever. Recent work, that
concentrated on the points of conflict and contact between quantum
theory and general relativity, suggests a new perspective on gravity. It
appears that the field equations of gravity in a wide class of theories
- including, but not limited to, standard Einstein's theory - can be
given a purely thermodynamic interpretation. In this approach gravity
appears as an emergent phenomenon, like e.g., gas or fluid dynamics. I
will describe the necessary background, key results, and their
implications. Mot(s) clés libre(s) : Gravity, General Relativity, Quantum Theory
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Rod Gover - Geometric Compactification, Cartan holonomy, and asymptotics
/ Fanny Bastien
/ Canal-u.fr
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Voir le résumé
Conformal compactification has long been recognised as an effective geometric framework for relating conformal geometry, and associated field theories ``at infinity'', to the asymptotic phenomena of an interior (pseudo-‐)-‐Riemannian geometry of one higher dimension. It provides an effective approach for analytic problems in GR, geometric scattering, conformal invariant theory, as well as the AdS/CFT correspondence of Physics. I will describe how the notion of conformal compactification can be linked to Cartan holonomy reduction. This leads to a conceptual way to define other notions of geometric compactification. The idea will be taken up, in particular, for the case of compactifying pseudo-‐ Riemannian manifolds using projective geometry. A new characterisation of projectively compact metrics will be given, and some results on their asymptotics near the conformal infinity. This is joint work with Andreas Cap. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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Rod Gover - An introduction to conformal geometry and tractor calculus (Part 4)
/ Fanny Bastien
/ 25-06-2014
/ Canal-u.fr
Gover Rod
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Voir le résumé
After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in this framework. Motivated by the need to develop a more effective approach to such problems we are led into the idea of conformal geometry and a conformally invariant calculus; this``tractor calculus'' is then developed explicitly. We will discuss how to calculate using this, and touch on applications to the construction of conformal invariants and conformally invariant differential operators. The second part of the course is concerned with the application of conformal geometry and tractor calculus for the treatment of conformal compactification and the geometry of conformal infinity. The link with Friedrich’s conformal field equations will be made. As part of this part we also dedicate some time to the general problem of treating hypersurfaces in a conformal manifold, and in particular arrive at a conformal Gauss equation. Finally we show how these tools maybe applied to treat aspects of the asymptotic analysis of boundary problems on conformally compact manifolds. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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Rod Gover - An introduction to conformal geometry and tractor calculus (Part 3)
/ Fanny Bastien
/ 25-06-2014
/ Canal-u.fr
Gover Rod
Voir le résumé
Voir le résumé
After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in this framework. Motivated by the need to develop a more effective approach to such problems we are led into the idea of conformal geometry and a conformally invariant calculus; this``tractor calculus'' is then developed explicitly. We will discuss how to calculate using this, and touch on applications to the construction of conformal invariants and conformally invariant differential operators. The second part of the course is concerned with the application of conformal geometry and tractor calculus for the treatment of conformal compactification and the geometry of conformal infinity. The link with Friedrich’s conformal field equations will be made. As part of this part we also dedicate some time to the general problem of treating hypersurfaces in a conformal manifold, and in particular arrive at a conformal Gauss equation. Finally we show how these tools maybe applied to treat aspects of the asymptotic analysis of boundary problems on conformally compact manifolds. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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Rod Gover - An introduction to conformal geometry and tractor calculus (Part 2)
/ Fanny Bastien
/ 24-06-2014
/ Canal-u.fr
Gover Rod
Voir le résumé
Voir le résumé
After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in this framework. Motivated by the need to develop a more effective approach to such problems we are led into the idea of conformal geometry and a conformally invariant calculus; this``tractor calculus'' is then developed explicitly. We will discuss how to calculate using this, and touch on applications to the construction of conformal invariants and conformally invariant differential operators. The second part of the course is concerned with the application of conformal geometry and tractor calculus for the treatment of conformal compactification and the geometry of conformal infinity. The link with Friedrich’s conformal field equations will be made. As part of this part we also dedicate some time to the general problem of treating hypersurfaces in a conformal manifold, and in particular arrive at a conformal Gauss equation. Finally we show how these tools maybe applied to treat aspects of the asymptotic analysis of boundary problems on conformally compact manifolds. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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