# Instructor guide: Stress-energy source and energy-condition ledger

Course: General relativity

Suggested time: 60–80 minutes

## Learning target

Learners translate geometry into a frame-declared source ledger and keep energy-condition diagnostics separate from engineering feasibility.

## Prepare

- Review Gμν=8πGTμν/c⁴ component by component.
- Define the orthonormal frame used by the model.
- Prepare one dimensional scaling estimate.

## Facilitation moves

- Require source units and frame labels.
- Separate local contractions from volume-integrated budgets.
- Ask what matter model could realize the inferred tensor.

## Misconception checks

- **Writing a metric automatically supplies a physical source.** Einstein's equation infers a stress-energy tensor; realizability, stability, preparation, and backreaction remain separate problems.
- **Negative coordinate density is an invariant fact.** Physical density is measured by a specified observer contraction, not an unlabeled coordinate component.

## Accessibility and participation

- Use a component ledger alongside tensor notation.
- Read index contractions aloud in observer language.
- Offer a scaling-first route before full equations.

## Evidence of learning

- A frame-declared source ledger
- A valid NEC calculation
- A geometry-versus-realizability distinction

## Extension

Construct a candidate scalar-field source and test whether its stress-energy reproduces the required eigenvalue pattern.

## Evidence boundary

Assess the learner's reasoning only within the declared model and recorded observations. Do not upgrade a simulation result into a claim about an unmodeled physical system.