An optimal transport formulation of the Einstein equations of general relativity
The goal of the paper is to give an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmological constant and the energy-momentum tensor. Such an optimal transport formulation is in terms of convexity/concavit...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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European Mathematical Society
2022
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| _version_ | 1826310154848567296 |
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| author | Mondino, A Suhr, S |
| author_facet | Mondino, A Suhr, S |
| author_sort | Mondino, A |
| collection | OXFORD |
| description | The goal of the paper is to give an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmological constant and the energy-momentum tensor. Such an optimal transport formulation is in terms of convexity/concavity properties of the Boltzmann–Shannon entropy along curves of probability measures extremizing suitable optimal transport costs. The result gives a new connection between general relativity and optimal transport; moreover, it gives a mathematical reinforcement of the strong link between general relativity and thermodynamics/information theory that emerged in the physics literature of the last years.
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| first_indexed | 2024-03-07T07:46:20Z |
| format | Journal article |
| id | oxford-uuid:085c07ed-4c21-4808-85cc-8811abcb3eac |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:46:20Z |
| publishDate | 2022 |
| publisher | European Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:085c07ed-4c21-4808-85cc-8811abcb3eac2023-06-20T11:19:02ZAn optimal transport formulation of the Einstein equations of general relativityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:085c07ed-4c21-4808-85cc-8811abcb3eacEnglishSymplectic Elements at OxfordEuropean Mathematical Society2022Mondino, ASuhr, SThe goal of the paper is to give an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmological constant and the energy-momentum tensor. Such an optimal transport formulation is in terms of convexity/concavity properties of the Boltzmann–Shannon entropy along curves of probability measures extremizing suitable optimal transport costs. The result gives a new connection between general relativity and optimal transport; moreover, it gives a mathematical reinforcement of the strong link between general relativity and thermodynamics/information theory that emerged in the physics literature of the last years. |
| spellingShingle | Mondino, A Suhr, S An optimal transport formulation of the Einstein equations of general relativity |
| title | An optimal transport formulation of the Einstein equations of general relativity |
| title_full | An optimal transport formulation of the Einstein equations of general relativity |
| title_fullStr | An optimal transport formulation of the Einstein equations of general relativity |
| title_full_unstemmed | An optimal transport formulation of the Einstein equations of general relativity |
| title_short | An optimal transport formulation of the Einstein equations of general relativity |
| title_sort | optimal transport formulation of the einstein equations of general relativity |
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