Vacuum solutions in the Einstein–Aether Theory
Bibliographic record
Abstract
The Einstein–Aether (EA) theory belongs to a class of modified gravity theories characterized by the introduction of a time-like unit vector field called aether. In this scenario, a preferred frame arises as a natural consequence of a broken Lorentz invariance. In the present work, we have obtained and analyzed some exact solutions allowed by this theory for two particular cases of a perfect fluid, both with Friedmann–Lemaître–Robertson–Walker symmetry: (i) a fluid with constant energy density (p = –ρ0) and (ii) a fluid with zero energy density (ρ0 = 0) corresponding to the vacuum solution with and without cosmological constant (Λ), respectively. Our solutions show that the EA and general relativity (GR) theories only differ in coupling constants. This difference is clearly shown because of the existence of singularities that are not in GR theory. This characteristic appears in the solutions with p = –ρ0 as well as with ρ0 = 0, where this last one depends only on the aether field. Furthermore, we consider the term of the EA theory in the Raychaudhuri equation and discuss the meaning of the strong energy condition in this scenario and found that this depends on the aether field. The solutions admit an expanding or contracting system. Bounce, singular, constant, and accelerated expansion solutions were also obtained, exhibiting the richness of the EA theory from the dynamic point of view of a collapsing system or of a cosmological model. The analysis of energy conditions, considering an effective fluid, shows that the term of the aether contributes significantly for the accelerated expansion of the system for the case in which the energy density is constant. On the other hand, for the vacuum case (ρ0 = 0), the energy conditions are all satisfied for the aether fluid.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".