Reduced geometry and its role in explicit spacetime symmetry violation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908362751344640 |
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| author | Reyes, Carlos M. Riquelme, César Schreck, Marco Soto, Alex |
| author_facet | Reyes, Carlos M. Riquelme, César Schreck, Marco Soto, Alex |
| contents | The incompatibility of explicit diffeomorphism violation with Riemannian geometry within the gravitational Standard-Model Extension (SME) is revisited. We review two methods of how to deal with this problem. The first is based on an approach proposed originally by Stückelberg and the latter is to restrict spacetime geometry via the dynamical field equations and the second Bianchi identities. Moreover, a third technique is introduced in this work, which relies on isometries of a gravitational system. Our conclusion is that an SME background field configuration compatible with Riemannian geometry is more likely to be determined the more diffeomorphisms are isometries of the particular system. The proposal is demonstrated to work for cosmological time evolution with the SME backgrounds $u$ and $s^{μν}$ present. This finding has the potential to provide an alternative treatment of explicit spacetime symmetry violation in gravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19264 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reduced geometry and its role in explicit spacetime symmetry violation Reyes, Carlos M. Riquelme, César Schreck, Marco Soto, Alex General Relativity and Quantum Cosmology High Energy Physics - Theory The incompatibility of explicit diffeomorphism violation with Riemannian geometry within the gravitational Standard-Model Extension (SME) is revisited. We review two methods of how to deal with this problem. The first is based on an approach proposed originally by Stückelberg and the latter is to restrict spacetime geometry via the dynamical field equations and the second Bianchi identities. Moreover, a third technique is introduced in this work, which relies on isometries of a gravitational system. Our conclusion is that an SME background field configuration compatible with Riemannian geometry is more likely to be determined the more diffeomorphisms are isometries of the particular system. The proposal is demonstrated to work for cosmological time evolution with the SME backgrounds $u$ and $s^{μν}$ present. This finding has the potential to provide an alternative treatment of explicit spacetime symmetry violation in gravity. |
| title | Reduced geometry and its role in explicit spacetime symmetry violation |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.19264 |