Einstein–æther models III: conformally static metrics, perfect fluid and scalar fields
Bibliographic record
Abstract
Abstract The asymptotic properties of conformally static metrics in Einstein–æther theory with a perfect fluid source and a scalar field are analyzed. In case of perfect fluid, some relativistic solutions are recovered such as: Minkowski spacetime, the Kasner solution, a flat FLRW space and static orbits depending on the barotropic parameter $$\gamma $$ γ . To analyze locally the behavior of the solutions near a sonic line $$v^2=\gamma -1$$ v 2 = γ - 1 , where v is the tilt, a new “shock” variable is used. Two new equilibrium points on this line are found. These points do not exist in General Relativity when $$1<\gamma <2 $$ 1 < γ < 2 . In the limiting case of General Relativity these points represent stiff solutions with extreme tilt. Lines of equilibrium points associated with a change of causality of the homothetic vector field are found in the limit of general relativity. For non-homogeneous scalar field $$\phi (t,x)$$ ϕ ( t , x ) with potential $$V(\phi (t,x))$$ V ( ϕ ( t , x ) ) the symmetry of the conformally static metric restrict the scalar fields to be considered to $$ \phi (t,x)=\psi (x)-\lambda t, V(\phi (t,x))= e^{-2 t} U(\psi (x))$$ ϕ ( t , x ) = ψ ( x ) - λ t , V ( ϕ ( t , x ) ) = e - 2 t U ( ψ ( x ) ) , $$U(\psi )=U_0 e^{-\frac{2 \psi }{\lambda }}$$ U ( ψ ) = U 0 e - 2 ψ λ . An exhaustive analysis (analytical or numerical) of the stability conditions is provided for some particular cases.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".