(Generalized) quasi-topological gravities at all orders
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Bibliographic record
Abstract
Abstract A new class of higher-curvature modifications of )-dimensional Einstein gravity has been recently identified. Densities belonging to this ‘Generalized quasi-topological’ class (GQTGs) are characterized by possessing non-hairy generalizations of the Schwarzschild black hole satisfying and by having second-order equations of motion when linearized around maximally symmetric backgrounds. GQTGs for which the equation of the metric function is algebraic are called ‘Quasi-topological’ and only exist for . In this paper we prove that GQTG and Quasi-topological densities exist in general dimensions and at arbitrarily high curvature orders. We present recursive formulas which allow for the systematic construction of n th order densities of both types from lower order ones, as well as explicit expressions valid at any order. We also obtain the equation satisfied by for general D and n . Our results here tie up the remaining loose end in the proof presented in Bueno et al (2019 (arXiv:1906.00987)) that every gravitational effective action constructed from arbitrary contractions of the metric and the Riemann tensor is equivalent, through a metric redefinition, to some GQTG.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it