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>