From Relativistic Gravity to the Poisson Equation
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910627522412544 |
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| author | Bergshoeff, Eric A. Giorgi, Giacomo Romano, Luca |
| author_facet | Bergshoeff, Eric A. Giorgi, Giacomo Romano, Luca |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00692 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From Relativistic Gravity to the Poisson Equation Bergshoeff, Eric A. Giorgi, Giacomo Romano, Luca High Energy Physics - Theory 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. |
| title | From Relativistic Gravity to the Poisson Equation |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.00692 |