From relativistic gravity to the Poisson equation
Abstract We consider the non-relativistic limit of general relativity coupled to a (p+1)-form gauge field and a scalar field in arbitrary dimensions and investigate under which conditions this gives rise to a Poisson equation for a Newton potential describing Newton-Cartan gravity outside a massive...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP02(2025)015 |
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| author | Eric A. Bergshoeff Giacomo Giorgi Luca Romano |
| author_facet | Eric A. Bergshoeff Giacomo Giorgi Luca Romano |
| author_sort | Eric A. Bergshoeff |
| collection | DOAJ |
| description | Abstract We consider the non-relativistic limit of general relativity coupled to a (p+1)-form gauge field and a scalar field in arbitrary dimensions and investigate under which conditions this gives rise to a Poisson equation for a Newton potential describing Newton-Cartan gravity outside a massive p-dimensional extended object, a so-called p-brane. Given our Ansatz, we show that not all the p-branes satisfy the required conditions. We study theories whose dynamics is defined by a Lagrangian as well as systems that are defined by a set of equations of motion not related to a Lagrangian. We show that, within the Lagrangian approach, a Poisson equation can be obtained provided that the coupling of the scalar field is fine-tuned such that the non-relativistic Lagrangian is invariant under an emerging local dilatation symmetry. On the other hand, we demonstrate that in the absence of a Lagrangian a Poisson equation can be obtained from a set of equations of motion that is not dilatation invariant. We discuss how our Ansatz could be generalized such as to include more p-branes giving rise to a Poisson equation. |
| format | Article |
| id | doaj-art-01a2abf74fed4db9bc2f1a1acb94893a |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-01a2abf74fed4db9bc2f1a1acb94893a2025-02-09T12:08:35ZengSpringerOpenJournal of High Energy Physics1029-84792025-02-012025214210.1007/JHEP02(2025)015From relativistic gravity to the Poisson equationEric A. Bergshoeff0Giacomo Giorgi1Luca Romano2Van Swinderen Institute, University of GroningenDepartamento de Física, Universidad de MurciaDepartamento de Electromagnetismo y Electronica, Universidad de MurciaAbstract We consider the non-relativistic limit of general relativity coupled to a (p+1)-form gauge field and a scalar field in arbitrary dimensions and investigate under which conditions this gives rise to a Poisson equation for a Newton potential describing Newton-Cartan gravity outside a massive p-dimensional extended object, a so-called p-brane. Given our Ansatz, we show that not all the p-branes satisfy the required conditions. We study theories whose dynamics is defined by a Lagrangian as well as systems that are defined by a set of equations of motion not related to a Lagrangian. We show that, within the Lagrangian approach, a Poisson equation can be obtained provided that the coupling of the scalar field is fine-tuned such that the non-relativistic Lagrangian is invariant under an emerging local dilatation symmetry. On the other hand, we demonstrate that in the absence of a Lagrangian a Poisson equation can be obtained from a set of equations of motion that is not dilatation invariant. We discuss how our Ansatz could be generalized such as to include more p-branes giving rise to a Poisson equation.https://doi.org/10.1007/JHEP02(2025)015Classical Theories of GravityGauge SymmetryP-Branes |
| spellingShingle | Eric A. Bergshoeff Giacomo Giorgi Luca Romano From relativistic gravity to the Poisson equation Journal of High Energy Physics Classical Theories of Gravity Gauge Symmetry P-Branes |
| title | From relativistic gravity to the Poisson equation |
| title_full | From relativistic gravity to the Poisson equation |
| title_fullStr | From relativistic gravity to the Poisson equation |
| title_full_unstemmed | From relativistic gravity to the Poisson equation |
| title_short | From relativistic gravity to the Poisson equation |
| title_sort | from relativistic gravity to the poisson equation |
| topic | Classical Theories of Gravity Gauge Symmetry P-Branes |
| url | https://doi.org/10.1007/JHEP02(2025)015 |
| work_keys_str_mv | AT ericabergshoeff fromrelativisticgravitytothepoissonequation AT giacomogiorgi fromrelativisticgravitytothepoissonequation AT lucaromano fromrelativisticgravitytothepoissonequation |