Nonsingular solutions to the Einstein equations on piecewise-Lorentzian manifolds
Bibliographic record
Abstract
We consider 4-dimensional spacetime manifolds that are piecewise Lorentzian, where the Lorentzian components of the manifold are separated by codimension-one planes (spacelike or timelike) on which the metric is degenerate. Such manifolds are of interest because they enlarge the smooth and nonsingular solution space of the Einstein equations. Planes of degeneracy that are perpendicular to each other can exist simultaneously. We describe various solutions of this type to the vacuum equations ${G}_{\ensuremath{\mu}\ensuremath{\nu}}=0$ and ${G}_{\ensuremath{\mu}\ensuremath{\nu}}+\mathrm{\ensuremath{\Lambda}}{g}_{\ensuremath{\mu}\ensuremath{\nu}}=0$, and to ${G}_{\ensuremath{\mu}\ensuremath{\nu}}=8\ensuremath{\pi}G{T}_{\ensuremath{\mu}\ensuremath{\nu}}$ for a perfect fluid. Novel examples include static gravitational lumps of finite curvature and a spacetime that responds to a cosmological constant via oscillations in time and/or space. A spacelike degeneracy plane can be used to avoid the big bang singularity, as we have further described elsewhere.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 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".