Conservation of asymptotic charges from past to future null infinity: supermomentum in general relativity
Abstract We show that the BMS-supertranslations and their associated supermomenta on past null infinity can be related to those on future null infinity, proving the conjecture of Strominger for a class of spacetimes which are asymptotically-flat in the sense of Ashtekar and Hansen. Using a cylindric...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP03(2019)148 |
| _version_ | 1818934467451944960 |
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| author | Kartik Prabhu |
| author_facet | Kartik Prabhu |
| author_sort | Kartik Prabhu |
| collection | DOAJ |
| description | Abstract We show that the BMS-supertranslations and their associated supermomenta on past null infinity can be related to those on future null infinity, proving the conjecture of Strominger for a class of spacetimes which are asymptotically-flat in the sense of Ashtekar and Hansen. Using a cylindrical 3-manifold of both null and spatial directions of approach towards spatial infinity, we impose appropriate regularity conditions on the Weyl tensor near spatial infinity along null directions. The asymptotic Einstein equations on this 3-manifold and the regularity conditions imply that the relevant Weyl tensor components on past null infinity are antipodally matched to those on future null infinity. The subalgebra of totally fluxless supertranslations near spatial infinity provides a natural isomorphism between the BMS-supertranslations on past and future null infinity. This proves that the flux of the supermomenta is conserved from past to future null infinity in a classical gravitational scattering process provided additional suitable conditions are satisfied at the timelike infinities. |
| first_indexed | 2024-12-20T05:04:44Z |
| format | Article |
| id | doaj.art-3f8d787ef15c4bfd8e29562df85c2f74 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-20T05:04:44Z |
| publishDate | 2019-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-3f8d787ef15c4bfd8e29562df85c2f742022-12-21T19:52:26ZengSpringerOpenJournal of High Energy Physics1029-84792019-03-012019314810.1007/JHEP03(2019)148Conservation of asymptotic charges from past to future null infinity: supermomentum in general relativityKartik Prabhu0Cornell Laboratory for Accelerator-based Sciences and Education (CLASSE), Cornell UniversityAbstract We show that the BMS-supertranslations and their associated supermomenta on past null infinity can be related to those on future null infinity, proving the conjecture of Strominger for a class of spacetimes which are asymptotically-flat in the sense of Ashtekar and Hansen. Using a cylindrical 3-manifold of both null and spatial directions of approach towards spatial infinity, we impose appropriate regularity conditions on the Weyl tensor near spatial infinity along null directions. The asymptotic Einstein equations on this 3-manifold and the regularity conditions imply that the relevant Weyl tensor components on past null infinity are antipodally matched to those on future null infinity. The subalgebra of totally fluxless supertranslations near spatial infinity provides a natural isomorphism between the BMS-supertranslations on past and future null infinity. This proves that the flux of the supermomenta is conserved from past to future null infinity in a classical gravitational scattering process provided additional suitable conditions are satisfied at the timelike infinities.http://link.springer.com/article/10.1007/JHEP03(2019)148Classical Theories of GravityGauge SymmetryGlobal SymmetriesSpaceTime Symmetries |
| spellingShingle | Kartik Prabhu Conservation of asymptotic charges from past to future null infinity: supermomentum in general relativity Journal of High Energy Physics Classical Theories of Gravity Gauge Symmetry Global Symmetries SpaceTime Symmetries |
| title | Conservation of asymptotic charges from past to future null infinity: supermomentum in general relativity |
| title_full | Conservation of asymptotic charges from past to future null infinity: supermomentum in general relativity |
| title_fullStr | Conservation of asymptotic charges from past to future null infinity: supermomentum in general relativity |
| title_full_unstemmed | Conservation of asymptotic charges from past to future null infinity: supermomentum in general relativity |
| title_short | Conservation of asymptotic charges from past to future null infinity: supermomentum in general relativity |
| title_sort | conservation of asymptotic charges from past to future null infinity supermomentum in general relativity |
| topic | Classical Theories of Gravity Gauge Symmetry Global Symmetries SpaceTime Symmetries |
| url | http://link.springer.com/article/10.1007/JHEP03(2019)148 |
| work_keys_str_mv | AT kartikprabhu conservationofasymptoticchargesfrompasttofuturenullinfinitysupermomentumingeneralrelativity |