Numerical simulations of instabilities in general relativity
Why this work is in the frame
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Bibliographic record
Abstract
General relativity, one of the pillars of our understanding of the universe, has been a remarkably successful theory. It has stood the test of time for more than 100 years and has passed all experimental tests so far. Most recently, the LIGO collaboration made the first-ever direct detection of gravitational waves, confirming a long-standing prediction of general relativity. Despite this, several fundamental mathematical questions remain unanswered, many of which relate to the global existence and the stability of solutions to Einstein’s equations. This thesis presents our efforts to use numerical relativity to investigate some of these questions. We present a complete picture of the end points of black ring instabilities in five dimensions. Fat rings collapse to Myers-Perry black holes. For intermediate rings, we discover a previously unknown instability that stretches the ring without changing its thickness and causes it to collapse to a Myers-Perry black hole. Most importantly, however, we find that for very thin rings, the Gregory-Laflamme instability dominates and causes the ring to break. This provides the first concrete evidence that in higher dimensions, the weak cosmic censorship conjecture may be violated even in asymptotically flat spacetimes. For Myers-Perry black holes, we investigate instabilities in five and six dimensions. In six dimensions, we demonstrate that both axisymmetric and non-axisymmetric instabilities can cause the black hole to pinch off, and we study the approach to the naked singularity in detail. Another question that has attracted intense interest recently is the instability of anti-de Sitter space. In this thesis, we explore how breaking spherical symmetry in gravitational collapse in anti-de Sitter space affects black hole formation. These findings were made possible by our new open source general relativity code, GRChombo, whose adaptive mesh capabilities allow accurate simulations of phenomena in which new length scales are produced dynamically. In this thesis, we describe GRChombo in detail, and analyse its performance on the latest supercomputers. Furthermore, we outline numerical advances that were necessary for simulating higher dimensional black holes stably and efficiently.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it