Hodge Dual Gauge Symmetry in Minimal Einstein-Aether Theory
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910968438587392 |
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| author | Hajian, Kamal |
| author_facet | Hajian, Kamal |
| contents | Einstein-aether gravity is a theory that breaks the local Lorentz symmetry by introducing a preferred direction via a vector field, which is considered to play the role of an aether. The theory is identified by four coupling constants between the aether and gravity. Minimal Einstein-aether is the special case in which only one of the couplings is non-zero. We show that the aether vector field in its minimal version is Hodge dual to a gauge field. The gauge symmetry in the dual description has been known for decades and has been used to implement a cosmological constant into the Lagrangian. As a result, solutions to the well-established gauge theory can be transferred into the minimal Einstein-aether theory straightforwardly. On the other hand, some of the proposed solutions to the minimal Einstein-aether theory could be discarded as pure gauges of the vanishing aether. We prove as a theorem that this holds true for all divergence-less aether fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_12641 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hodge Dual Gauge Symmetry in Minimal Einstein-Aether Theory Hajian, Kamal General Relativity and Quantum Cosmology High Energy Physics - Theory Einstein-aether gravity is a theory that breaks the local Lorentz symmetry by introducing a preferred direction via a vector field, which is considered to play the role of an aether. The theory is identified by four coupling constants between the aether and gravity. Minimal Einstein-aether is the special case in which only one of the couplings is non-zero. We show that the aether vector field in its minimal version is Hodge dual to a gauge field. The gauge symmetry in the dual description has been known for decades and has been used to implement a cosmological constant into the Lagrangian. As a result, solutions to the well-established gauge theory can be transferred into the minimal Einstein-aether theory straightforwardly. On the other hand, some of the proposed solutions to the minimal Einstein-aether theory could be discarded as pure gauges of the vanishing aether. We prove as a theorem that this holds true for all divergence-less aether fields. |
| title | Hodge Dual Gauge Symmetry in Minimal Einstein-Aether Theory |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.12641 |