On the KG-constrained general disformal transformation of the Einstein-Hilbert action
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910757903400960 |
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| author | Alinea, Allan L. Ordonez, Joshwa DJ. |
| author_facet | Alinea, Allan L. Ordonez, Joshwa DJ. |
| contents | Although with great successes in explaining phenomena and natural behaviour involving the Universe or a part thereof, the General Theory of Relativity is far from a complete theory. Focusing on its extension within the framework of scalar tensor theory, we investigate the transformation of the Einstein-Hilbert action under the general disformal transformation coupled with a set of triple KG constraints. The idea is that the general disformal transformation leads to an extremely complicated action necessitating a set of constraints to tame the resulting form. Motivated by previous studies on the invertibility and invariance of the massless Klein-Gordon equation under the general disformal transformation, we identify three constraints that significantly simplifies the transformed Einstein-Hilbert action. In four spacetime dimensions, we find that the transformed action is a sum of the original action and a disformal contribution involving a six-term Lagrangian that includes the Ricci tensor coupled to a sum of derivatives of scalar fields and kinetic terms. In three spacetime dimensions, the disformal contribution becomes a five-term Lagrangian. Lastly, in two spacetime dimensions, the Einstein-Hilbert action is invariant under the constrained disformal transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06176 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the KG-constrained general disformal transformation of the Einstein-Hilbert action Alinea, Allan L. Ordonez, Joshwa DJ. General Relativity and Quantum Cosmology Although with great successes in explaining phenomena and natural behaviour involving the Universe or a part thereof, the General Theory of Relativity is far from a complete theory. Focusing on its extension within the framework of scalar tensor theory, we investigate the transformation of the Einstein-Hilbert action under the general disformal transformation coupled with a set of triple KG constraints. The idea is that the general disformal transformation leads to an extremely complicated action necessitating a set of constraints to tame the resulting form. Motivated by previous studies on the invertibility and invariance of the massless Klein-Gordon equation under the general disformal transformation, we identify three constraints that significantly simplifies the transformed Einstein-Hilbert action. In four spacetime dimensions, we find that the transformed action is a sum of the original action and a disformal contribution involving a six-term Lagrangian that includes the Ricci tensor coupled to a sum of derivatives of scalar fields and kinetic terms. In three spacetime dimensions, the disformal contribution becomes a five-term Lagrangian. Lastly, in two spacetime dimensions, the Einstein-Hilbert action is invariant under the constrained disformal transformation. |
| title | On the KG-constrained general disformal transformation of the Einstein-Hilbert action |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2408.06176 |