Classical and quantum decay of oscillations: Oscillating self-gravitating real scalar field solitons
Bibliographic record
Abstract
The oscillating gravitational field of an oscillaton of finite mass M causes it to lose energy by emitting classical scalar field waves, but at a rate that is nonperturbatively tiny for small $\ensuremath{\mu}\ensuremath{\equiv}GMm/\ensuremath{\Elzxh}c,$ where m is the scalar field mass: $dM/dt\ensuremath{\approx}\ensuremath{-}3797{437.776(c}^{3}/G){\ensuremath{\mu}}^{\ensuremath{-}2}{e}^{\ensuremath{-}39.433795197/\ensuremath{\mu}}[1+O(\ensuremath{\mu})].$ Oscillatons also decay by the quantum process of the annihilation of scalarons into gravitons, which is only perturbatively small in $\ensuremath{\mu},$ giving by itself $dM/dt\ensuremath{\approx}\ensuremath{-}0.008513223{935(m}^{2}{c}^{2}/\ensuremath{\Elzxh}){\ensuremath{\mu}}^{5}[1+O({\ensuremath{\mu}}^{2})].$ Thus the quantum decay is faster than the classical one for $\ensuremath{\mu}\ensuremath{\lesssim}39.4338/[\mathrm{ln}(\ensuremath{\Elzxh}{c/Gm}^{2})+7\mathrm{ln}(1/\ensuremath{\mu})+19.9160].$ The time for an oscillaton to decay away completely into free scalarons and gravitons is ${t}_{\mathrm{decay}}\ensuremath{\sim}2{\ensuremath{\Elzxh}}^{6}{c}^{3}{/G}^{5}{m}^{11}\ensuremath{\sim}{10}^{324}\mathrm{yr}(1\mathrm{meV}{/mc}^{2}{)}^{11}.$ Oscillatons of more than one real scalar field of the same mass generically asymptotically approach a static-geometry $U(1)$ boson star configuration with $\ensuremath{\mu}={\ensuremath{\mu}}_{0},$ at the rate ${d(GM/c}^{3})/dt\ensuremath{\approx}[(C/{\ensuremath{\mu}}^{4}{)e}^{\ensuremath{-}\ensuremath{\alpha}/\ensuremath{\mu}}{+Q(m/m}_{\mathrm{Pl}}{)}^{2}{\ensuremath{\mu}}^{3}]({\ensuremath{\mu}}^{2}\ensuremath{-}{\ensuremath{\mu}}_{0}^{2}),$ with ${\ensuremath{\mu}}_{0}$ depending on the magnitudes and relative phases of the oscillating fields, and with the same constants C, $\ensuremath{\alpha},$ and Q given numerically above for the single-field case that is equivalent to ${\ensuremath{\mu}}_{0}=0.$
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".