Summary
This paper explores a duality between minimal Einstein-aether theory, which breaks local Lorentz symmetry via a preferred vector field, and the gauge field formulation of the cosmological constant. This connection facilitates solution transfers and discards non-physical, divergence-less aether fields.
Highlights
- Einstein-aether gravity introduces a preferred direction, breaking local Lorentz invariance.
- The Levi-Civita tensor and Hodge duality play key roles in formulating the theory.
- Minimal Einstein-aether theory’s field equations are derived from the principle of least action.
- The cosmological constant is formulated as a gauge field in Einstein gravity.
- The 3-form gauge field is identified as the Hodge dual of the aether 1-form field.
- Divergence-less aether fields are shown to be non-physical and can be discarded.
- The duality enables transferring known solutions, including Kerr-Newman (A)dS black holes, between the two frameworks.
Key Insights
- Lorentz Symmetry Breaking via Aether Field: The introduction of a unit timelike vector field breaks local Lorentz invariance, offering a modified gravity framework while maintaining general covariance. This preferred direction redefines local rest frames and impacts dynamics.
- Use of Hodge Duality: By expressing the aether vector field’s Hodge dual as a 3-form gauge field, the theory reveals a gauge symmetry structure that parallels cosmological constant formulations, enriching the mathematical framework.
- Gauge Formulation of Cosmological Constant: Modeling the cosmological constant as a gauge field with associated field strength provides a novel perspective, connecting vacuum energy with gauge symmetries and facilitating modified gravitational dynamics.
- Equations of Motion and Solutions: The minimal Einstein-aether equations are akin to Einstein gravity with additional aether contributions. This allows embedding solutions like (anti)-de Sitter Kerr-Newman black holes with aether fields into the framework, illustrating its physical relevance.
- Identification of Pure Gauge Solutions: The duality clarifies the distinction between physical and pure gauge aether configurations, specifically proving that divergence-less aether fields do not represent physical states, thus refining the solution space.
- Implications for Modified Gravity Theories: This work deepens understanding of vector-tensor theories that modify gravity by introducing preferred directions, potentially relevant for explaining dark sectors or Lorentz-violating phenomena.
- Facilitating Solution Transfers: The established duality acts as a tool to translate solutions and symmetries between Einstein-aether theory and gauge field formulations, enhancing analytical tractability and physical interpretation.
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Citation
Hajian, K. (2025). Hodge Dual Gauge Symmetry in Minimal Einstein-Aether Theory (Version 1). arXiv. http://doi.org/10.48550/ARXIV.2504.12641