Level 5 · Graduate study · advanced assessment
Geometry-to-source feasibility review
Translate an exotic line element into source, tidal, and observational requirements before discussing engineering.
Complete all three challenges. Show assumptions, units, uncertainty, and the boundary between calculation, model-dependent inference, observation, and unresolved claim.
Challenge 1 · derivation
Derive the throat requirements
For a static spherical wormhole ansatz, derive the throat and flare-out conditions and evaluate the radial null-energy contraction at the throat. Preserve frame and sign conventions throughout.
Required deliverables
- • Geometric derivation from the metric functions
- • Throat-limit stress-energy relation
- • A convention audit and two sanity checks
Scoring criteria · 20 points
- • Geometry and throat conditions: 8 points
- • Stress-energy contraction: 7 points
- • Conventions and checks: 5 points
Challenge 2 · analysis
Search the source-tidal trade space
Sweep throat size and shape parameters to compare integrated source requirement, peak null-energy violation, tidal acceleration, and crossing time. Identify Pareto-efficient points without naming any point feasible unless every declared gate passes.
Required deliverables
- • A sweep of at least 30 parameter points
- • Four gate metrics and a Pareto plot
- • A feasibility table with pass, fail, or unresolved labels
Scoring criteria · 20 points
- • Correctly computed trade metrics: 7 points
- • Pareto and gate logic: 7 points
- • No feasibility overclaim: 6 points
Challenge 3 · design
Separate exotic lensing from ordinary structure
Design an observing program for a restricted exotic-metric lensing signature and a matched conventional mass-distribution alternative. Include selection effects, reconstruction bias, and a result that would disfavor the exotic model.
Required deliverables
- • Competing forward models and observable contrast
- • Injection-recovery and selection-bias tests
- • Preregistered model-comparison and follow-up rules
Scoring criteria · 20 points
- • Models make distinct predictions: 7 points
- • Bias controls and simulations: 7 points
- • Symmetric decision rules: 6 points
Instructor solution outlines
Look for reasoning that survives inspection
1. Derive the throat requirements
- • Apply the minimum-radius and flare-out requirements to the shape function.
- • Use the field equation to express the radial null contraction in geometric terms.
- • State that a geometric construction is not evidence that the required source exists or is controllable.
2. Search the source-tidal trade space
- • Compute geometry, source, and traversal quantities from the same parameter record.
- • Reject points that optimize one metric by silently worsening another.
- • Reserve unresolved for missing material or stability evidence rather than converting it to pass.
3. Separate exotic lensing from ordinary structure
- • Simulate both models through the same instrument and reconstruction pipeline.
- • Blind the injected class during pipeline tuning.
- • Treat an unexplained anomaly as unresolved until conventional structure and systematics are quantitatively excluded.