Tractor Geometry of Asymptotically Flat Spacetimes
In a recent work it was shown that conformal Carroll geometries are canonically equipped with a null-tractor bundle generalizing the tractor bundle of conformal geometry. We here show that in the case of the conformal boundary of an asymptotically flat spacetime of any dimension d ≥ 3 , this null-tr...
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Veröffentlicht in: | Annales Henri Poincaré 2022-09, Vol.23 (9), p.3265-3310 |
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description | In a recent work it was shown that conformal Carroll geometries are canonically equipped with a null-tractor bundle generalizing the tractor bundle of conformal geometry. We here show that in the case of the conformal boundary of an asymptotically flat spacetime of any dimension
d
≥
3
, this null-tractor bundle over null infinity can be canonically derived from the interior spacetime geometry. As was previously discussed, compatible normal connections on the null-tractor bundle are not unique: We prove that they are in fact in one-to-one correspondence with the germ of the asymptotically flat spacetimes to leading order. In dimension
d
=
3
the tractor connection invariantly encodes a choice of mass and angular momentum aspect, in dimension
d
≥
4
a choice of asymptotic shear. In dimension
d
=
4
the presence of tractor curvature correspond to gravitational radiation. Even thought these results are by construction geometrical and coordinate invariant, we give explicit expressions in BMS coordinates for concreteness. |
doi_str_mv | 10.1007/s00023-022-01174-0 |
format | Article |
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d
≥
3
, this null-tractor bundle over null infinity can be canonically derived from the interior spacetime geometry. As was previously discussed, compatible normal connections on the null-tractor bundle are not unique: We prove that they are in fact in one-to-one correspondence with the germ of the asymptotically flat spacetimes to leading order. In dimension
d
=
3
the tractor connection invariantly encodes a choice of mass and angular momentum aspect, in dimension
d
≥
4
a choice of asymptotic shear. In dimension
d
=
4
the presence of tractor curvature correspond to gravitational radiation. Even thought these results are by construction geometrical and coordinate invariant, we give explicit expressions in BMS coordinates for concreteness.</description><identifier>ISSN: 1424-0637</identifier><identifier>EISSN: 1424-0661</identifier><identifier>DOI: 10.1007/s00023-022-01174-0</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Angular momentum ; Asymptotic properties ; Classical and Quantum Gravitation ; Dynamical Systems and Ergodic Theory ; Elementary Particles ; Geometry ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematical Physics ; Mathematics ; Physics ; Physics and Astronomy ; Quantum Field Theory ; Quantum Physics ; Relativity ; Relativity Theory ; Spacetime ; Theoretical ; Tractors</subject><ispartof>Annales Henri Poincaré, 2022-09, Vol.23 (9), p.3265-3310</ispartof><rights>Springer Nature Switzerland AG 2022</rights><rights>Springer Nature Switzerland AG 2022.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c353t-5ff6010024543f424e0e9a74b27bdc5e12c4c2935359c25d210ae0989c5b5b323</citedby><cites>FETCH-LOGICAL-c353t-5ff6010024543f424e0e9a74b27bdc5e12c4c2935359c25d210ae0989c5b5b323</cites><orcidid>0000-0002-5646-4301</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00023-022-01174-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00023-022-01174-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,776,780,881,27903,27904,41467,42536,51298</link.rule.ids><backlink>$$Uhttps://hal.science/hal-03883363$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Herfray, Yannick</creatorcontrib><title>Tractor Geometry of Asymptotically Flat Spacetimes</title><title>Annales Henri Poincaré</title><addtitle>Ann. Henri Poincaré</addtitle><description>In a recent work it was shown that conformal Carroll geometries are canonically equipped with a null-tractor bundle generalizing the tractor bundle of conformal geometry. We here show that in the case of the conformal boundary of an asymptotically flat spacetime of any dimension
d
≥
3
, this null-tractor bundle over null infinity can be canonically derived from the interior spacetime geometry. As was previously discussed, compatible normal connections on the null-tractor bundle are not unique: We prove that they are in fact in one-to-one correspondence with the germ of the asymptotically flat spacetimes to leading order. In dimension
d
=
3
the tractor connection invariantly encodes a choice of mass and angular momentum aspect, in dimension
d
≥
4
a choice of asymptotic shear. In dimension
d
=
4
the presence of tractor curvature correspond to gravitational radiation. Even thought these results are by construction geometrical and coordinate invariant, we give explicit expressions in BMS coordinates for concreteness.</description><subject>Angular momentum</subject><subject>Asymptotic properties</subject><subject>Classical and Quantum Gravitation</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Elementary Particles</subject><subject>Geometry</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematical Physics</subject><subject>Mathematics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Relativity</subject><subject>Relativity Theory</subject><subject>Spacetime</subject><subject>Theoretical</subject><subject>Tractors</subject><issn>1424-0637</issn><issn>1424-0661</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kDFPwzAQhS0EEqXwB5giMTEEzuc4iceqoi1SJQbKbDmuA6mSOtguUv49LkFlY7qn03fvnR4htxQeKEDx6AEAWQqIKVBaZCmckQnNMIo8p-cnzYpLcuX9DoBiycSE4MYpHaxLlsZ2JrghsXUy80PXBxsardp2SBatCslrr7QJTWf8NbmoVevNze-ckrfF02a-Stcvy-f5bJ1qxllIeV3nEJ_DjGesjvEGjFBFVmFRbTU3FHWmUUSWC418ixSUAVEKzSteMWRTcj_6fqhW9q7plBukVY1czdbyuANWlozl7ItG9m5ke2c_D8YHubMHt4_vSSyAAS1zcaRwpLSz3jtTn2wpyGOPcuxRxh7lT48xY0rYeOQjvH837s_6n6tvF69yWQ</recordid><startdate>20220901</startdate><enddate>20220901</enddate><creator>Herfray, Yannick</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-5646-4301</orcidid></search><sort><creationdate>20220901</creationdate><title>Tractor Geometry of Asymptotically Flat Spacetimes</title><author>Herfray, Yannick</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c353t-5ff6010024543f424e0e9a74b27bdc5e12c4c2935359c25d210ae0989c5b5b323</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Angular momentum</topic><topic>Asymptotic properties</topic><topic>Classical and Quantum Gravitation</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Elementary Particles</topic><topic>Geometry</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematical Physics</topic><topic>Mathematics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Relativity</topic><topic>Relativity Theory</topic><topic>Spacetime</topic><topic>Theoretical</topic><topic>Tractors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Herfray, Yannick</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Annales Henri Poincaré</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Herfray, Yannick</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Tractor Geometry of Asymptotically Flat Spacetimes</atitle><jtitle>Annales Henri Poincaré</jtitle><stitle>Ann. Henri Poincaré</stitle><date>2022-09-01</date><risdate>2022</risdate><volume>23</volume><issue>9</issue><spage>3265</spage><epage>3310</epage><pages>3265-3310</pages><issn>1424-0637</issn><eissn>1424-0661</eissn><abstract>In a recent work it was shown that conformal Carroll geometries are canonically equipped with a null-tractor bundle generalizing the tractor bundle of conformal geometry. We here show that in the case of the conformal boundary of an asymptotically flat spacetime of any dimension
d
≥
3
, this null-tractor bundle over null infinity can be canonically derived from the interior spacetime geometry. As was previously discussed, compatible normal connections on the null-tractor bundle are not unique: We prove that they are in fact in one-to-one correspondence with the germ of the asymptotically flat spacetimes to leading order. In dimension
d
=
3
the tractor connection invariantly encodes a choice of mass and angular momentum aspect, in dimension
d
≥
4
a choice of asymptotic shear. In dimension
d
=
4
the presence of tractor curvature correspond to gravitational radiation. Even thought these results are by construction geometrical and coordinate invariant, we give explicit expressions in BMS coordinates for concreteness.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00023-022-01174-0</doi><tpages>46</tpages><orcidid>https://orcid.org/0000-0002-5646-4301</orcidid></addata></record> |
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source | Springer Nature - Complete Springer Journals |
subjects | Angular momentum Asymptotic properties Classical and Quantum Gravitation Dynamical Systems and Ergodic Theory Elementary Particles Geometry Mathematical and Computational Physics Mathematical Methods in Physics Mathematical Physics Mathematics Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Relativity Theory Spacetime Theoretical Tractors |
title | Tractor Geometry of Asymptotically Flat Spacetimes |
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