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The contracted Bianchi identity states that the sum of three applications of this operation to the Riemann tensor yields zero. For 10 points each:
[10h] Name this operation denoted in index notation by a semicolon. The Levi–Civita (“LAY-vee CHEE-vee-ta”) connection is chosen so that this operation is zero when applied to the metric.
ANSWER: covariant derivative [prompt on derivative; reject “directional derivative”]
[10e] The contracted Bianchi identities state that the covariant derivative of a tensor named for this physicist is zero. This physicist’s namesake “field equations” are central to general relativity.
ANSWER: Albert Einstein [accept Einstein field equations or Einstein tensor]
[10m] The Einstein tensor is defined as this tensor minus one-half the scalar curvature times the metric tensor. Contracting the first and third indices of the Riemann tensor produces this tensor.
ANSWER: Ricci tensor [or Ricci curvature tensor]
<JC, Physics>

EditionsHeardPPBEasy %Medium %Hard %
13813.9587%40%13%

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TeamOpponentPart 1Part 2Part 3TotalParts
Cambridge DCambridge B010010E
Imperial BLSE0000
Oxford AWarwick B0101020EM
Oxford CSouthampton A0000
SheffieldBristol010010E

Summary

TournamentEditionHeardPPBEasy %Medium %Hard %
California2025-02-01310.0067%33%0%
Lower Mid-Atlantic2025-02-01615.00100%33%17%
Midwest2025-02-01616.6783%50%33%
Northeast2025-02-01516.00100%40%20%
Pacific Northwest2025-02-01220.00100%50%50%
South Central2025-02-01215.00100%50%0%
Southeast2025-02-01120.00100%100%0%
UK2025-02-0158.0060%20%0%
Upper Mid-Atlantic2025-02-01812.5088%38%0%