<?xml version="1.0" encoding="UTF-8"?><metadata>
<lom xmlns="http://ltsc.ieee.org/xsd/LOM" xmlns:lomfr="http://www.lom-fr.fr/xsd/LOMFR" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://ltsc.ieee.org/xsd/LOM http://www.lom-fr.fr/xsd/lomfrv1.0/std/lomfr.xsd">
<general>
    <identifier>
        <catalog>Canal-U_Ocms</catalog>
        <entry>22569</entry>
    </identifier>
    <title><string language="fre"><![CDATA[Thomas Backdahl - Symmetry operators, conserved currents and energy momentum tensors]]></string></title>
    <language>ENG</language>
    <description>
        <string language="fre"><![CDATA[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.]]></string></description>
    <keyword><string language="fre"><![CDATA[mathématiques]]></string></keyword><keyword><string language="fre"><![CDATA[Grenoble]]></string></keyword><keyword><string language="fre"><![CDATA[école d'été]]></string></keyword><keyword><string language="fre"><![CDATA[General Relativity]]></string></keyword><keyword><string language="fre"><![CDATA[institut fourier]]></string></keyword><keyword><string language="fre"><![CDATA[summer school]]></string></keyword><keyword><string language="fre"><![CDATA[asymptotic analysis]]></string></keyword>
    <lomfr:documentType>
        <lomfr:source>LOMFRv1.0</lomfr:source>
        <lomfr:value>image en mouvement</lomfr:value>
    </lomfr:documentType>
</general><lifeCycle>
    
    <contribute>
            <role>
                <source>LOMv1.0</source>
                <value>author</value>
            </role>
            <entity><![CDATA[BEGIN:VCARD
VERSION:3.0
CLASS:PUBLIC
REV:2016-06-12 00:01:57
FN:Thomas Backdahl
N:Backdahl;Thomas;;;

URL;TYPE=work:http://www.maths.ed.ac.uk/~tbackdah/
ROLE:author
TZ:+0200
END:VCARD
]]></entity>
            <date><dateTime>2014-07-04</dateTime></date>
        </contribute>

    <contribute>
            <role>
                <source>LOMv1.0</source>
                <value>content provider</value>
            </role>
            <entity><![CDATA[BEGIN:VCARD
VERSION:3.0
CLASS:PUBLIC
REV:2016-06-12 00:01:57
FN:Fanny Bastien
N:Bastien;Fanny;;;

URL;TYPE=work:http://www.canal-u.tv/auteurs/bastien_fanny
ROLE:content provider
TZ:+0200
END:VCARD
]]></entity>
            <date><dateTime>2014-07-04</dateTime></date>
        </contribute>

</lifeCycle>
<metaMetadata>
    <metadataSchema>LOMv1.0</metadataSchema>
    <metadataSchema>LOMFRv1.0</metadataSchema>
</metaMetadata>
<technical>
    <format>video/x-flv</format>
    <location><![CDATA[http://www.canal-u.tv/video/institut_fourier/thomas_backdahl_symmetry_operators_conserved_currents_and_energy_momentum_tensors.22569]]></location>
    <location><![CDATA[rtmpt://fms2.cerimes.fr:80/vod/institut_fourier/thomas.backdahl.symmetry.operators.conserved.currents.and.energy.momentum.tensors_22569/backdhal_ecoleete_04072014_sd.mp4]]></location>
        
        
    <size>1725405935</size>
    <duration><duration>PT0H44M19S</duration></duration>
</technical>
<educational>
    <learningResourceType>
        <source>LOMv1.0</source>
        <value>lecture</value>
    </learningResourceType>
    
    <context>
        <source>LOMv1.0</source>
        <value>doctorat</value>
    </context>
</educational>
<rights>
    <cost>
        <source>LOMv1.0</source>
        <value>no</value>
    </cost>
    <copyrightAndOtherRestrictions>
        <source>LOMv1.0</source>
        <value>no</value>
    </copyrightAndOtherRestrictions>
    <description>
        <string language="fre"><![CDATA[Droits réservés à l'éditeur et aux auteurs. 
CC BY-NC-ND 4.0]]></string>
    </description>
</rights>

            <relation>
                <kind>
                    <source>LOMv1.0</source>
                    <value>ispartof</value>
                </kind>
                <resource>
                    <identifier>
                        <catalog>URI</catalog>
                        <entry>http://www.canal-u.tv/producteurs/institut_fourier/ecoles_d_ete</entry>
                    </identifier>
                    <description>
                        <string language="fre"><![CDATA[Ecoles d'été]]></string>
                    </description>
                </resource>
            </relation>

            <relation>
                <kind>
                    <source>LOMv1.0</source>
                    <value>ispartof</value>
                </kind>
                <resource>
                    <identifier>
                        <catalog>URI</catalog>
                        <entry>http://www.canal-u.tv/producteurs/institut_fourier/ecoles_d_ete</entry>
                    </identifier>
                    <description>
                        <string language="fre"><![CDATA[2014]]></string>
                    </description>
                </resource>
            </relation>

<classification>
    <purpose>
        <source>LOMv1.0</source>
        <value>discipline</value>
    </purpose>
    <taxonPath>
        <source>
        <string language="fre"><![CDATA[Universités Numériques Thématiques 2009 http://www.universites-numeriques.fr]]></string>
        </source>
        <taxon>
            <id/>
            <entry>
                <string language="fre"/>
            </entry>
        </taxon>
    </taxonPath>
</classification>
<classification>
    <purpose>
        <source>LOMv1.0</source>
        <value>discipline</value>
    </purpose>
    
    <taxonPath>
        <source>
            <string language="fre">CDD 22e éd.</string>
            <string language="eng">DDC 22nd ed.</string>
        </source>
        <taxon>
            <id>510</id>
            <entry>
                <string language="fre"><![CDATA[Mathématiques]]></string>
            </entry>
        </taxon>
   </taxonPath>
</classification>      </lom>
   </metadata>