Teleparallel gravity from the principal bundle viewpoint
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917501355425792 |
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| author | Brezina, Sebastian Boffo, Eugenia Krššák, Martin |
| author_facet | Brezina, Sebastian Boffo, Eugenia Krššák, Martin |
| contents | We examine whether the Teleparallel Equivalent of General Relativity (TEGR) can be formulated as a gauge theory in the language of connections on principal bundles. We argue in favor of using either the affine bundle with the Poincaré group or, equivalently, the orthonormal frame bundle with the Lorentz group as the structure group. Following the framework of Trautman--where gauge symmetries are determined using the absolute elements--we set to identify the absolute elements and gauge symmetries of TEGR. The problem of a non-dynamical teleparallel connection raises the question of whether it should be treated as an absolute element. If so, the gauge group of TEGR is potentially some undetermined subgroup of the diffeomorphism group. On the other hand, if the connection is allowed to be non-dynamical but the only absolute element is taken to be the canonical 1-form of the frame bundle, we recover the whole diffeomorphism group as the gauge group of TEGR. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Teleparallel gravity from the principal bundle viewpoint Brezina, Sebastian Boffo, Eugenia Krššák, Martin General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We examine whether the Teleparallel Equivalent of General Relativity (TEGR) can be formulated as a gauge theory in the language of connections on principal bundles. We argue in favor of using either the affine bundle with the Poincaré group or, equivalently, the orthonormal frame bundle with the Lorentz group as the structure group. Following the framework of Trautman--where gauge symmetries are determined using the absolute elements--we set to identify the absolute elements and gauge symmetries of TEGR. The problem of a non-dynamical teleparallel connection raises the question of whether it should be treated as an absolute element. If so, the gauge group of TEGR is potentially some undetermined subgroup of the diffeomorphism group. On the other hand, if the connection is allowed to be non-dynamical but the only absolute element is taken to be the canonical 1-form of the frame bundle, we recover the whole diffeomorphism group as the gauge group of TEGR. |
| title | Teleparallel gravity from the principal bundle viewpoint |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2507.23672 |