Smooth and sharp creation of a spherical shell for a (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>)-dimensional quantum field
Bibliographic record
Abstract
We study the creation of a spherical, finite radius source for a quantized massless scalar field in $3+1$ dimensions. The goal is to model the breakdown of correlations that has been proposed to occur at the horizon of an evaporating black hole. We do this by introducing at fixed radius $r=a$ a one parameter family of self-adjoint extensions of the three dimensional Laplacian operator that interpolate between the condition that the values and the derivatives on the two sides of $r=a$ coincide for $t\ensuremath{\le}0$ (no wall) and the two-sided Dirichlet boundary condition for $t\ensuremath{\ge}1/\ensuremath{\lambda}$ (fully-developed wall). Creation of the shell produces null, spherical pulses of energy on either side of the shell, one ingoing and the other outgoing. The renormalized energy density $⟨{T}_{00}⟩$ diverges to positive infinity in the outgoing energy pulse, just outside the light cone of the fully-formed wall at $t=1/\ensuremath{\lambda}$. Unlike in the $3+1$ point source creation, there is no persistent memory cloud of energy. As in the creation of a $1+1$ dimensional wall, the response of an Unruh-DeWitt detector in the post-shell region is independent of the time scale for shell formation and is finite. The latter property casts doubt on the efficacy of this mechanism for firewall creation.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| 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".