Rigidity of marginally outer trapped surfaces in Reissner-Nordström spacetime
Bibliographic record
Abstract
Our primary focus in this thesis is to investigate the stability vs rigidity of marginally outer trapped surfaces (MOTS) in four-dimensional Reissner-Nordström (RN) spacetime. This is connected to studying the first-order derivative of the stability operator (and hence the second derivative of the outgoing null expansion). Stability means that the principal eigenvalue is non-negative, and rigidity means that we cannot deform MOTS. The question we have addressed in this thesis is distinguishing between stability and rigidity. We study the special case of the inner horizon of Reissner-Nordström spacetimes for specific values of charge and mass is horizons can be unstable, and we ask questions whether they unstable is still rigid. To approach this question we use a technique to reduce an infinite-dimensional second variation calculation to a finite-dimensional one. We start with a brief introduction to general relativity and review some fundamental aspects of black holes. We then define the stability of MOTS in terms of the principal eigenvalue. Since the stability operator has a zero eigenvalue in our case, the MOTS admits infinitesimal deformations. In the rest of the work we use Lyapunov-Schmidt reduction to investigate whether these infinitesimal deformations can be made finite. We give evidence that suggests that the inner horizon is stable.
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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 | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".