Effective loop quantum gravity framework for vacuum spherically symmetric spacetimes
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Bibliographic record
Abstract
We develop an effective framework for the $\overline{\ensuremath{\mu}}$ scheme of holonomy corrections motivated by loop quantum gravity for vacuum spherically symmetric space-times. This is done by imposing the areal gauge in the classical theory and then expressing the remaining components of the Ashtekar-Barbero connection in the Hamiltonian constraint in terms of holonomies of physical length ${\ensuremath{\ell}}_{\mathrm{Pl}}$. The stationary solutions to the effective Hamiltonian constraint can be found exactly, and we give the explicit form of the effective metric in Painlev\'e-Gullstrand coordinates. This solution has the correct classical limit, the quantum gravity corrections decay rapidly at large distances, and curvature scalars are bounded by the Planck scale, independently of the black hole mass $M$. In addition, the solution is valid for radii $x\ensuremath{\ge}{x}_{\mathrm{min}}\ensuremath{\sim}({\ensuremath{\ell}}_{\mathrm{Pl}}^{2}M{)}^{1/3}$ indicating the need for a matter field, with an energy density bounded by the Planck scale, to provide a source for the curvature in the space-time. Finally, for $M\ensuremath{\gg}{m}_{\mathrm{Pl}}$, the space-time has an outer and also an inner horizon, within which the expansion for outgoing radial null geodesics becomes positive again. On the other hand, for sufficiently small $M\ensuremath{\sim}{m}_{\mathrm{Pl}}$, there are no horizons at all in the effective metric.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 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 | 0.001 |
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