Asymptotic safety in quantum gravity and diffeomorphic non-isometric metric solutions to the Schwarzschild metric
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Bibliographic record
Abstract
We revisit the construction of diffeomorphic but not isometric metric solutions to the Schwarzschild metric. These solutions require the introduction of non-trivial areal–radial functions and are characterized by the key property that the radial horizon’s location is displaced continuously towards the singularity (r = 0). In the limiting case scenario the location of the singularity and horizon merges and any in-falling observer hits a null singularity at the very moment they cross the horizon. This fact may have important consequences for the resolution of the fire wall problem and the complementarity controversy in black holes. This construction allows us to borrow the results over the past two decades pertaining to the study of the renormalization group improvement of Einstein’s equations, which was based on the possibility that quantum Einstein gravity may be non-perturbatively renormalizable and asymptotically safe because of the presence of interacting (non-Gaussian) ultraviolet fixed points. The particular areal–radial function that eliminates the interior of a black hole, and furnishes a truly static metric solution everywhere, is used to establish the desired energy-scale relation k = k(r), which is obtained from the k (energy) dependent modifications to the running Newtonian coupling G(k), cosmological constant Λ(k), and space–time metric g ij ,( k ) (x). (Anti) de Sitter – Schwarzschild metrics are also explored as examples. We conclude with a discussion of the role that asymptotic safety may have in the geometry of phase spaces (cotangent bundles of space–time) (i.e., in establishing a quantum space–time geometry or classical phase geometry correspondence g ij,(k) (x) ↔ g ij (x, E)).
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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