Notice
Thomas Backdahl - Symmetry operators, conserved currents and energy momentum tensors
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
Descriptif
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.
Documentation
Liens
Dans la même collection
-
Philippe G LeFloch - Weakly regular spacetimes with T2 symmetry
LEFLOCH Philippe G.
I will discuss the initial value problem for the Einstein equations and present results concerning the existence and asymptotic behavior of
-
Andras Vasy - Microlocal analysis and wave propagation (Part 4)
In these lectures I will explain the basics of microlocal analysis, emphasizing non elliptic problems, such as wave propagation, both on manifolds without boundary, and on manifolds with boundary. In
-
Claudio Dappiaggi - On the role of asymptotic structures in the construction of quantum states for …
DAPPIAGGI Claudio
In the algebraic approach to quantum field theory on curved backgrounds, there exists a special class of quantum states for free fields,
-
Andras Vasy - Microlocal analysis and wave propagation (Part 1)
VASY András
In these lectures I will explain the basics of microlocal analysis, emphasizing non elliptic problems, such as wave propagation, both on
-
Jérémie Joudioux - Hertz potentials and the decay of higher spin fields
JOUDIOUX Jérémie
The study of the asymptotic behavior of higher spin fields has proven to be a key point in understanding the stability properties of
-
Alain Bachelot - Waves in the Anti-de Sitter space-time Ads
BACHELOT Alain
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
-
Lionel Mason - Perturbative formulae for scattering of gravitational wave
MASON Lionel J.
The Christodoulou Klainerman proof of existence of asymptotically simple space-times shows that it is reasonable to consider the scattering of
-
Andras Vasy - Microlocal analysis and wave propagation (Part 3)
In these lectures I will explain the basics of microlocal analysis, emphasizing non elliptic problems, such as wave propagation, both on manifolds without boundary, and on manifolds with boundary. In
-
Alexander Strohmaier - Workshop
STROHMAIER Alexander
I will explain how one can formulate and formalize the Gupta Bleuler framework for the Quantization of the electromagnetic field in an
-
-
Jérémie Szeftel - General relativity (Workshop)
SZEFTEL Jérémie
In order to control locally a space time which satisfies the Einstein equations, what are the minimal assumptions one should make on its
-
Sur le même thème
-
"Le mathématicien Petre (Pierre) Sergescu, historien des sciences, personnalité du XXe siècle"
HERLéA Alexandre
Alexandre HERLEA est membre de la section « Sciences, histoire des sciences et des techniques et archéologie industrielle » du CTHS. Professeur émérite des universités, membre effectif de l'Académie
-
Webinaire sur la rédaction des PGD
LOUVET Violaine
Rédaction des Plans de Gestion de Données (PGD) sous l’angle des besoins de la communauté mathématique.
-
Alexandre Booms : « Usage de matériel pédagogique adapté en géométrie : une transposition à interro…
« Usage de matériel pédagogique adapté en géométrie : une transposition à interroger ». Alexandre Booms, doctorant (Université de Reims Champagne-Ardenne - Cérep UR 4692)
-
P. Burkhardt - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow
BURKHARDT-GUIM Paula
We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second
-
R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions
BAMLER Richard H.
We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow.
-
C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
LI Chao
In this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC
-
Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wings
LAI Yi
We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at
-
T. Ozuch - Noncollapsed degeneration and desingularization of Einstein 4-manifolds
OZUCH Tristan
We study the noncollapsed singularity formation of Einstein 4-manifolds. We prove that any smooth Einstein 4-manifold close to a singular one in a mere Gromov-Hausdorff (GH) sense is the result
-
D. Tewodrose - Limits of Riemannian manifolds satisfying a uniform Kato condition
TEWODROSE David
Presentation of a joint work with G. Carron and I. Mondello where we study Kato limit spaces.
-
A. Mondino - Time-like Ricci curvature bounds via optimal transport
MONDINO Andrea
The goal of the talk is to present a recent work in collaboration with Cavalletti (SISSA) on optimal transport in Lorentzian synthetic spaces. The aim is to set up a “Lorentzian analog” of the
-
M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem
LESOURD Martin
The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. A major role has been played by Gromov's results and conjectures, and in
-
J. Wang - Topological rigidity and positive scalar curvature
WANG Jian
In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with