Continuity equations for general matter: applications in numerical relativity
Due to the absence of symmetries under time and spatial translations in a general curved spacetime, the energy and momentum of matter is not conserved as it is in flat space. This means, for example, that the flux of matter energy through a surface is in general not balanced by an equal increase in...
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| Format: | Journal article |
| Language: | English |
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IOP Publishing
2021
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| _version_ | 1797107396072439808 |
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| author | Clough, K |
| author_facet | Clough, K |
| author_sort | Clough, K |
| collection | OXFORD |
| description | Due to the absence of symmetries under time and spatial translations in a general curved spacetime, the energy and momentum of matter is not conserved as it is in flat space. This means, for example, that the flux of matter energy through a surface is in general not balanced by an equal increase in the energy of the matter contained within the enclosed volume—there is an additional 'source' resulting from the curvature of spacetime acting on the matter (and vice versa). One can calculate this source term and reconcile the flux and energy accumulation over time in an arbitrary volume, although a foliation of the spacetime must be chosen, making the quantities inherently coordinate dependent. Despite this dependence, these quantities are practically useful in numerical relativity simulations for a number of reasons. We provide expressions for general matter sources in a form appropriate for implementation in the Arnowitt Deser Misner decomposition, and discuss several applications in simulations of compact object dynamics and cosmology. |
| first_indexed | 2024-03-07T07:13:56Z |
| format | Journal article |
| id | oxford-uuid:7d7b9666-7b9a-4e7f-be50-f53ac35b46c5 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:13:56Z |
| publishDate | 2021 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:7d7b9666-7b9a-4e7f-be50-f53ac35b46c52022-07-26T09:45:49ZContinuity equations for general matter: applications in numerical relativityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7d7b9666-7b9a-4e7f-be50-f53ac35b46c5EnglishSymplectic ElementsIOP Publishing2021Clough, KDue to the absence of symmetries under time and spatial translations in a general curved spacetime, the energy and momentum of matter is not conserved as it is in flat space. This means, for example, that the flux of matter energy through a surface is in general not balanced by an equal increase in the energy of the matter contained within the enclosed volume—there is an additional 'source' resulting from the curvature of spacetime acting on the matter (and vice versa). One can calculate this source term and reconcile the flux and energy accumulation over time in an arbitrary volume, although a foliation of the spacetime must be chosen, making the quantities inherently coordinate dependent. Despite this dependence, these quantities are practically useful in numerical relativity simulations for a number of reasons. We provide expressions for general matter sources in a form appropriate for implementation in the Arnowitt Deser Misner decomposition, and discuss several applications in simulations of compact object dynamics and cosmology. |
| spellingShingle | Clough, K Continuity equations for general matter: applications in numerical relativity |
| title | Continuity equations for general matter: applications in numerical relativity |
| title_full | Continuity equations for general matter: applications in numerical relativity |
| title_fullStr | Continuity equations for general matter: applications in numerical relativity |
| title_full_unstemmed | Continuity equations for general matter: applications in numerical relativity |
| title_short | Continuity equations for general matter: applications in numerical relativity |
| title_sort | continuity equations for general matter applications in numerical relativity |
| work_keys_str_mv | AT cloughk continuityequationsforgeneralmatterapplicationsinnumericalrelativity |