These things lend their name to an effect measured by (*) Gravity Probe B, in which a nonrotating mass drags vectors along with it.
A theorem describing conditions under which these things undergo focusing is used in the derivation of the Raychaudhuri equation. In a coordinate system named for these things, Christoffel symbols vanish. Killing vectors are the Noether currents of symmetries along these extremals. For physically-realizable ones, which are affinely parametrized by the proper time, its second derivative plus the sum of all permutations of its first derivatives under the Levi-Civita connection, is zero. Schild's ladder uses these things to approximate parallel transport along a curve. The rate of separation between two of these things is proportional to the Riemann curvature tensor. These things lend their name to an effect measured by (*) Gravity Probe B, in which a nonrotating mass drags vectors along with it. Massless particles travel along "null" ones, while timelike ones are the world-lines traversed by free particles. For 10 points, name these paths that generalize the notion of straight lines to curved spacetime, which see use in a certain architectural construction that approximates great circles on a sphere.
A theorem describing conditions under which these things undergo focusing is used in the derivation of the Raychaudhuri equation.
geodesics [prompt on "world-lines"]