Question
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>
Summary
| California | 2025-02-01 | Y | 3 | 10.00 | 67% | 33% | 0% |
| Lower Mid-Atlantic | 2025-02-01 | Y | 6 | 15.00 | 100% | 33% | 17% |
| Midwest | 2025-02-01 | Y | 6 | 16.67 | 83% | 50% | 33% |
| Northeast | 2025-02-01 | Y | 5 | 16.00 | 100% | 40% | 20% |
| Pacific Northwest | 2025-02-01 | Y | 2 | 20.00 | 100% | 50% | 50% |
| South Central | 2025-02-01 | Y | 2 | 15.00 | 100% | 50% | 0% |
| Southeast | 2025-02-01 | Y | 1 | 20.00 | 100% | 100% | 0% |
| Upper Mid-Atlantic | 2025-02-01 | Y | 8 | 12.50 | 88% | 38% | 0% |
Data
| Georgia Tech C | Bruin A | 0 | 10 | 10 | 20 |