Parallel Transport, Christoffel Symbols and the Geodesic Equation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Carrying arrows on curved ground

Science · Astronomy & Astrophysics · ages 23-24
Name ______________________   Date ____________
  1. Where do the Christoffel symbols come from?

    • They are guessed at random
    • They fall from the sky
    • From the metric
  2. How do you compare vectors at different points?

    • Overlap them by eye
    • Carry one with the rule
    • Vectors can never be compared
  3. A geodesic parallel-transports its own tangent.

    Circle one:   True   False

  4. What does the geodesic equation describe?

    • A rocket firing its engines
    • A free-fall path
    • A path that stops at once
  5. Why is the plain component change not enough for a derivative?

    • The basis changes too
    • Components never change anywhere
    • Derivatives are banned in curves
  6. What are the pieces of the geodesic equation?

    • Two unrelated constants
    • Only the metric alone
    • Corrected acceleration
  7. A friend calls any straight-looking coordinate line a geodesic. What is missing?

    • Lines must look curvy instead
    • It must carry its tangent
    • Coordinates decide everything
  8. A freely falling capsule feels no force yet follows a curve in coordinates. Explain.

    • Free fall on a geodesic
    • An invisible rope pulls it
    • Coordinates push all capsules
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Carrying arrows on curved ground W1-mt_bUEL2R91Vy-s1

  1. From the metric · Metric in, symbols out.
  2. Carry one with the rule · Comparison needs carrying first.
  3. True · That carrying is the definition.
  4. A free-fall path · Geodesic equals free fall.
  5. The basis changes too · Two things change: components and basis.
  6. Corrected acceleration · Acceleration corrected by the symbols.
  7. It must carry its tangent · Looks deceive; the equation decides.
  8. Free fall on a geodesic · Curved coordinates, straightest path.
Worksheet · LightMySky