Logarithmic catastrophes and Stokes’s phenomenon in waves at horizons
Bibliographic record
Abstract
Abstract Waves propagating near an event horizon display interesting features including logarithmic phase singularities and caustics. We consider an acoustic horizon in a flowing Bose–Einstein condensate where the elementary excitations obey the Bogoliubov dispersion relation. In the Hamiltonian ray theory the solutions undergo a broken pitchfork bifurcation near the horizon and one might therefore expect the associated wave structure to be given by a Pearcey function, this being the universal wave function that dresses catastrophes with two control parameters. However, the wave function is in fact an Airy-type function supplemented by a logarithmic phase term, a novel type of wave catastrophe. Similar wave functions arise in aeroacoustic flows from jet engines, path integrals in radio astronomy, and also gravitational horizons if dispersion which violates Lorentz symmetry in the UV is included. The approach we take differs from most previous authors in that we analyze the behavior of the integral representation of the wave function using exponential coordinates. This allows for a different treatment of the branch cuts and gives rise to an analysis based purely on saddlepoint expansions. We are thereby able to resolve the multiple real and complex waves that interact at the horizon and its companion caustic. We find that the horizon is a physical manifestation of a Stokes surface, marking the place where a wave is born, and that the horizon and the caustic do not in general coincide: the finite spatial region between them delineates a broadened horizon.
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How this classification was reachedexpand
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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".